Math 10

Approved by Government of Nepal, Ministry of Education, Curriculum Development Center,
Sano Thimi, Bhaktapur as an additional material.

10

10

Publisher
Oasis Publication Pvt. Ltd.
Copyright
The Publisher

Language Editor
Sedunath Dhakal

Edition
B.S. 2073 (2016 AD)
B.S. 2074 (2017 AD)
B.S. 2075 (2018 AD)
B.S. 2076 (2019 AD)
B.S. 2078 (2021 AD) (Completely revised)

Contributors
Megh Raj Adhikari
Man Bahadur Tamang
Laxmi Gautam

Layout
Oasis Desktop

Ramesh Bhattarai

Printed in Nepal

Preface

Oasis School Mathematics has been designed in compliance with the
latest curriculum of the Curriculum Development Center (CDC), the
Government of Nepal with a focus on child psychology of acquiring
mathematical knowledge and skill. The major thrust is on creating an
enjoyable experience in learning mathematics through the inclusion
of a variety of problems which are closely related to our daily life.
This book is expected to foster a positive attitude among children and
encourage them to enjoy mathematics. A conscious attempt has been
made to present mathematical concepts with ample illustrations,
assignments, activities, exercises and project work to the students in
a friendly manner to encourage them to participate actively in the
process of learning.

I have endeavored to present this book in a very simple and interesting
form. Exercises have been carefully planned. Enough exercises have
been presented to provide adequate practice.

I have tried to include the methods and ideas as suggested by the
teachers and subject experts who participated in the seminars, and
workshops conducted at different venues. I express my sincere
gratitude to my friends and well wishers for their valuable suggestions.

I am extremely grateful to Megh Raj Adhikari, Purusottam Bhatta,
Shuva Kumar Shrestha, Ananta Acharya, Prakash Ghimire, Shanta
Kumar Sen (Tamang), Man Bahadur Tamang, Laxmi Gautam and
Yadav Siwakoti for their invaluable suggestions and contributions.

Sincere gratitude to Managing Director Mr. Harish Chandra Bista
for his invaluable support and cooperation in getting this series
published in this shape.

In the end, constructive and practical suggestions of all kinds for
further improvement of the book will be appreciated and incorporated
in the course of revision.

Shyam Datta Adhikari
Author

March 2021

10

Contents

Sets ............................................................................................. 1

Unit : 1 Sets................................................................................................. 2
1.1 Warm-up Activities............................................................... 2
1.2 Set Operations........................................................................ 2
1.3 Cardinality of Finite Sets...................................................... 4

Arithmetic................................................................................... 23

Unit : 2 Tax and Money Exchange.......................................................... 24
2.1 Warm-up Activities............................................................... 24
2.1 Value Added Tax................................................................... 24
2.3 Money Exchange................................................................... 34
Unit : 3 Compound Interest..................................................................... 44
3.1 Warm-up Activities............................................................... 44
3.2 Compound Interest............................................................... 44
Unit : 4 Population Growth and Depreciation...................................... 63
4.1 Warm-up Activities............................................................... 63
4.2 Population Growth ............................................................... 63
4.3 Depreciation.......................................................................... 70

Mensuration............................................................................... 82

Unit : 5 Plane Surface................................................................................ 83
5.1 Warm up Activities................................................................ 83
5.2 Area of Triangle..................................................................... 83
Unit : 6 Cylinder, Sphere, Hemisphere and Cone................................ 94
6.1 Warm-up Activities.............................................................. 94
6.2 Cylinder................................................................................. 94
6.3 Sphere and Hemisphere...................................................... 102

6.4 Cone......................................................................................... 109
6.5 Combined Solids.................................................................... 116
Unit : 7 Prism and Pyramid...................................................................... 123
7.1 Warm-up Activities.............................................................. 123
7.2 Triangular Prism................................................................... 123
7.3 Pyramid................................................................................... 129
. 7.4 Combined Solids of Prism and Pyramid............................ 139
7.5 Geometrical Bodies................................................................ 145

Algebra......................................................................................... 161

Unit : 8 H.C.F. and L.C.M.......................................................................... 162
8.1 Warm-up Activities........................................................,....... 162
8.2 H.C.F......................................................................................... 162
8.3 L.C.M........................................................................................ 163
Unit : 9 Radical and Surds......................................................................... 170
9.1 Warm-up Activities................................................................ 170
9.2 Surds......................................................................................... 170
9.3 Rationalisation of Surds........................................................ 174
9.4 Equations Involving Surds.................................................... 178
Unit : 10 Indices............................................................................................ 184
10.1 Warm-up Activities.............................................................. 184
10.2 Indices.................................................................................... 184
10.3 Exponential Equations......................................................... 191
Unit : 11 Algebraic Fraction........................................................................ 195
11.1 Warm-up Activities.............................................................. 195
11.2 Simplification....................................................................... 195
Unit : 12 Equational Problems.................................................................... 201
12.1 Warm-up Activities.............................................................. 201
12.2 Simultaneous Equations...................................................... 201
12.3 Quadratic Equations............................................................ 211

Geometry...................................................................................... 225

Unit : 13 Area of Triangles and Parallelograms........................................ 226
13.1 Warm-up Activities.............................................................. 226
13.2 Base and Altitude of Triangle and Parallelogram............ 226
13.3 Area of Triangle..................................................................... 226
13.4 Area of Parallelogram.......................................................... 227

Contents

Unit : 14 Construction ................................................................................. 243

14.1 Warm-up Activities.............................................................. 243

14.2 Construction of a Parallelogram Equal in Area

with Given Parallelogram.................................................. 243

14.3 Construction of a Triangle Equal in Area with

Given Parallelogram .......................................................... 245

14.4 Construction of a Triangle Equal in Area with

Given Triangle....................................................................... 246

14.5 Construction of a Parallelogram Equal in Area with

Given Triangle........................................................................ 248

14.6 Construction of a Triangle Equal in Area with Given

Quadrilateral .......................................................................... 250

14.7 Construction of a Quadrilateral Equal in Area with

Given Triangle....................................................................... 251

Unit : 15 Circle................................................................................................. 253

15.1 Warm-up Activities................................................................. 253

15.2 Circle ........................................................................................ 253

15.3 Tangent and Secant................................................................. 284

Trigonometry................................................................................. 299

Unit : 16 Trigonometry................................................................................... 300

16.1 Warm-up Activities................................................................. 300

16.2 Area of Triangle....................................................................... 300

16.3 Height and Distance............................................................... 311

Statistics........................................................................................ 320

Unit : 17 Statistics............................................................................................ 321

17.1 Warm-up Activities................................................................. 321

17.2 Measures of Central Tendency.............................................. 321

17.3 Median...................................................................................... 325

17.4 Quartiles................................................................................... 329

17.5 Ogive (cumulative frequency curves).................................. 334

Probability........................................................................................................... 342

Unit : 18 Probability........................................................................................ 343

18.1 Warm-up Activities................................................................. 343

18.2 Probability................................................................................ 343

18.3 Independent events................................................................. 351

18.4 Tree diagram............................................................................ 355

Specification Grid.............................................................................................. 362

Model Test Paper................................................................................................ 363

Sets

8Estimated Teaching Hours

Contents

• Word problems on set using a Venn diagram of 2 sets
• Word problems on set using a Venn diagram of 3 sets

Expected Learning Outcomes

At the end of this unit, students will be able to develop the following
competencies:

• To solve the word problems on two sets using a
Venn diagram

• To solve the word problems on three sets using a
Venn diagram

Materials Required

• flash cards, chart paper, A4 size paper, sketch pen

Oasis School Mathematics-10 1

Unit

1 Sets

1.1 Warm-up Activities

Discuss the following in your class and draw a conclusion.

Observe the following Venn diagram and answer the questions given below.

Write the set of elements of A BU
(i) A (ii) B (iii) A and B both
(iv) A or B (v) neither A nor B •x •p •a •d
(vi) number of elements in each set. •y •q •b
•z •c

•e •f

1.2 Set Operations

Union of Sets

Let A and B be any two sets. The union of the two sets A and B is denoted by A ∪ B and
is defined as a set of elements which either belong to A or B or both.

A ∪ B is read as 'A union B' or 'A cup B'.

Symbolically,

A ∪ B = { x : x ∈ A or x ∈ B}.

Representation in Venn diagram:

A BU A U U
B A

B

(A∪B when A and B are overlapping) A∪B when A and B are disjoint A∪B where B is the subset of A

The shaded region in the Venn diagram represents A ∪ B.

Intersection of Sets:

Let A and B be any two sets. The intersection of the two sets A and B is denoted by A ∩
B and is defined as a set of elements which belong to A and B both.

A ∩ B is read as 'A intersection B' or 'A cap B'.

Symbolically,

A ∩ B = {x : x ∈ A and x ∈ B}

2 Oasis School Mathematics-10

Representation in Venn diagram:

A B U A U U
B A

B

(A∩B when A and B are overlapping) (A∩B when A and B are disjoint) (A∩B where B is the subset of A)
Th e shaded region in the Venn diagram represents A ∩ B.

Difference of Sets:
Let 'A' and 'B' be two sets. The difference of the two sets A and B is denoted by A – B and

is defined as a set of elements of A which do not belong to B.

A – B is read as 'A difference B' or 'A minus B'.

Symbolically, A – B = {x : x ∈ A and x ∉ B}.

Similarly, B – A = { x : x ∈ B and x ∉ A}.

A B U

The shaded region in the Venn diagram represents A – B.

A BU

The shaded region in the Venn diagram represents B – A.

Complement of Set

Let A be a subset of the universal set U. The complement of set A is denoted by A or Ac,
or A' and is defined as a set of elements of U which do not belong to A.

A is read as 'A bar' or 'a complement of set A in U'.
Symbolically, A = {x : x ∈ U and x ∉ A}.

A U

Symmetric Difference of Sets
Let A and B be two sets. The symmetric difference of the two sets A and B is denoted by

A∆B and is defined as the union of the differences A–B and B–A.
A∆B is read as 'A delta B'
Symbolically,

Oasis School Mathematics-10 3

A∆B = (A – B) ∪ (B – A)
= {x : x ∈ A – B or x∈B – A}

A BU

The shaded region in the Venn diagram represents A ∆ B.

Note : A∆B = (A ∪ B) – (A ∩ B)

1.3 Cardinality of finite sets A BU

The number of distinct elements in a finite set is called the cardinal 3 2 4
number of a set. 5 86
7 10
Hence, the cardinal number of a set is the number of elements
present in that set. 1

Observe the given Venn diagram.
Find the number of elements in set A.
A = {2, 3, 5, 7}. Set A has 4 elements. The cardinal number of set A is 4. Symbolically n(A) = 4
Similarly, find n(B), n(A∩B), n(A∪B), and n(A∪B).

Cardinal number of union of two sets A BU
Let A and B be any two overlapping sets such that x–z z y–z

n(A) = x
y
n(B) = z
x–z and n(B–A) = y–z
and n(A∩B) =
x–z+z+y–z
then n(A–B) = x+y–z
n(A) + n(B) – n(A∩B)
From the Venn diagram, n(A) + n(B) – n(A∩B)

n(A∪B) = 0

=

=

Hence, n(A∪B) =

If A and B are disjoint sets,

n(A∩B) =

Then, n(A∪B) = n(A) + n(B)

Some important results of cardinality of two sets:

A BU

n(A–B) or n0(A) n(B–A) or n0(B)
n(A∪B) n(A∪B)

n(A∩B)

4 Oasis School Mathematics-10

(i) n(A∪B) = n(A) + n(B) – n(A∩B)

(ii) n(A∪B) = n(A) + n(B) [If A and B are disjoint sets]

(iii) n(A–B) = n0(A) = n(A) – n(A∩B)

(iv) n(B–A) = n0(B) = n(B) – n(B∩A)
(v) n(A–B) = n0(A) = n(A∪B) – n(B)
(vi) n(B–A) = n0(B) = n(A∪B) – n(A)
(vii) n(A∪B) = n0(A) + n0(B) + n(A∩B)
(viii) n(A∪B) = n(U) – n(A∪ B)
(ix) n(A∆B) = n(A – B) + n (B–A)

(x) n(A∆B) = n(A ∪ B) – n (B ∩ A)

Remember !

Verbal form Set notations

* number of elements in either A or B or both n(A∪B)

* number of elements in at least one of A or B n(A∪B)

* number of elements in both sets A and B n(A∩B)

* number of elements only in set A n0(A) or n(A–B)
* number of elements in A but not in B n0(A) or n(A–B)
* number of elements only in set B n0(B) or n(B–A)
* number of elements in B but not in A n0(B) or n(B–A)
* number of elements neither in A nor in B
* number of elements in exactly one set n(A∪B)
n0(A) + n0(B)

Note:∩ A BU

• If two sets 'A' and 'B' are disjoint, U
BA

n(A∪B) = n(A) + n(B) and n (A∩B) = 0
∴ n(A∪B) has maximum value
and n(A∩B) has minimum value.
• If B A, n(A∪B) = n(A) and n(A∩B) = n(B)
∴ n(A∪B) has minimum value.
n(A∩B) has maximum value.

Oasis School Mathematics-10 5

Worked Out Examples

Example: 1
A and B are the subsets of the universal set 'U' in which n(U) = 50, n(A) = 32, n(B) = 25

and n(A∩B) = 15.
(i) Illustrate the above information in a Venn diagram.
(ii) Find the value of n(A∪B).
Solution:

Given, n(U) = 50, n(A) = 32, n(B) = 25, n(A∩B) = 15

Let n(A ∪ B) = x

Illustration in a Venn diagram: A BU

From the Venn diagram 32–15 15 25–15
= 17 =10
n(U) = 17 + 15 +10 + x
x
or, 50 = 42 + x

or, x = 50 – 42

or, x = 8

∴ n(A ∪ B) = 8

Example: 2

If n(A) = 45, n(B) = 65, n(A∪B) = 85,

(i) find n(A∩B), n0(A) and n0(B).
(ii) Illustrate the above information in a Venn diagram.
Solution:

(i) Here, n(A) = 45, n(B) = 65, n(A∪B) = 85.

We have, n(A∪B) = n(A) + n(B) – n(A∩B)

or, 85 = 45 + 65 – n(A∩B)

or, n(A∩B) = 45 + 65 – 85

or, n(A∩B) = 110 – 85

∴ n(A∩B) = 25

Again, n0(A) = n(A) – n(A∩B)

= 45 – 25

= 20

n0(B) = n(B) – n(A∩B)

= 65 – 25 A BU
20 25 40
= 40

(ii) Illustration in a Venn diagram

6 Oasis School Mathematics-10

A lternative method A BU
( i) Here, n(A) = 45, n(B) = 65, n(A∪B) = 85 45–x x 65–x

Let, n(A∩B) = x A BU
20 25 40
From the Venn diagram,

n(A∪B) = 45–x+x+65–x

or, 85 = 45+65–x

or, 85 = 110–x

or, x = 110–85

or, x = 25

∴ n(A∩B) = 25

Again, from the Venn diagram, n0(A) = 45–x = 45–25 = 20

n0(B) = 65–x = 65–25 = 40

(ii) Illustration in a Venn diagram

Example: 3

If n(A) = 20, n(B) = 15, find the maximum value of n(A∪B) and n(A∩B). U
Solution: B
Here, the value of n(A∪B) will be maximum when A

two sets are disjoint. 20 15
So, n(A∪B) = n(A) + n(B)

= 20 + 15 = 35

Again, the maximum value of n(A∩B) exists if one set is a subset of another.

So, if B⊂A then n(A∩B) = n(B) = 15. AU
Hence, the maximum value of n(A∩B) = 15. B

Example: 4

In a class of 55 students, 15 students liked Maths but not English, and 18 students
liked English but not Maths. If 5 students did not like both, how many students liked
both subjects? Represent the above information in a Venn diagram.

Solution:

Let M and E be the sets of students who liked Maths and English respectively.

Here, n0 (M) = n(M–E) = 15
n0(E) = n(E–M) = 18

n(M ∪ E) = 5

n (U) = 55

Oasis School Mathematics-10 7

Let, n(M∩E) = ?
n(U) = n0(M) + n0(E) + n(M∩E) + n(M ∪ E)
We have, 55 = 15 + 18 + 5 + n(M∩E)

or, 55 = 38 + n(M∩E)

or, n(M∩E) = 55 – 38 = 17

or,

So, 17 students liked both the subjects.

Representation in a Venn diagram is as shown in the figure.

M EU

15 17 18
5

Alternative method
Let M and E be the sets of students who liked Maths and English respectively.

Here, n0 (M) = 15, n0(E) = 18 M EU
n(M∪E) = 5, n(U) = 55 15 x 18
Let, n(M∩E) = x

From the Venn diagram, 5

15 + x + 18 + 5 = 55

or, x = 55 – 38 = 17

Representation in a Venn diagram is as shown in the figure.

M EU

15 17 18
5

Example 5

In an examination, 80% of the students passed in Mathematics, 70% passed in
Science and 10% failed in both subjects. Using a Venn diagram, find the percentage
of students who passed both subjects.

Solution:

Let 'M' and 'S' be the sets of students who passed in Mathematics and Science respectively.

Let, n(U) = 100
then, n(M) = 80, n(S) = 70, n(M ∪ S) = 10

n(M∩S) = ?

8 Oasis School Mathematics-10

n(M∩S) = x (suppose) A BU

Now, 80–x x 70–x
10

From the Venn diagram,

80 – x + x + 70 – x + 10 = n(U)

or, 160 – x = 100

or, x = 160 – 100

or, x = 60

∴ n(M∩S) = 60

Hence, 60% students passed in both subjects.

Example: 6
In a group of people, 50% like tea, 70% like coffee, 10% don't like both and 120 like

both. By using a Venn diagram, find the total number of people on the survey.

Solution:

Let 'T' and 'C' be the sets of people who like tea and coffee respectively.

Let, n(U) = x 50 x
100 2
Given, n(T) = 50% of x = × x = U

TC

n(C) = 70% of x = 70 × x = 7x x – 120 120 7x –120
100 10 2 10

n(T ∩ C) = 120 x
10

n(T ∪ C) = 10% of x = 10 × x = x
100 10

From the Venn diagram,

n(U) = x – 120 + 120 + 7x – 120 + x
2 10 10

or, x = x + 7x – 120 + x
2 10 10

or, x + 7x + x – x = 120
2 10 10

or, 5x + 7x + x – 10x = 120
10

or, 3x = 120
10

or, 3x = 120 ×10

or, x = 120 ×10
3

or, x = 400

∴ Total number of people in the survey = 400.

Oasis School Mathematics-10 9

Example: 7

In a group of 70 people the ratio of people who like documentaries to the people who
like movies is 5:4. If 10 people like both and 8 people do not like both, using a Venn
diagram, find the number of people who like

(i) documentaries only. (ii) movies only.

Solution:

Let 'D' and 'M' be the sets of people who like documentaries and movies respectively.

Given, n(U) = 70
Let
n(D) = 5x and n(M) = 4x
n(D∩M) = 10, n(D ∪ M) = 8

Now, D MU
5x–10 10 4x–10

8

From the Venn diagram,

n(U) = 5 x− 10 + 10 + 4 x− 10 + 8

or, 70 = 9 x− 2
or, 9 x = 70 + 2

or, 9 x = 72

or, x = 72 = 8
9

∴ n0 (D) = 5x − 10
= 5 × 8 − 10

= 30

and n0 (M) = 4x − 10
= 4 × 8 − 10

= 22

Hence, 30 people like documentaries only and 22 like movies only.


Exercise 1.1 A f BU
g
a c h
1. From the given figure, verify that d i
b e
(i) n(A∪B) = n(A) + n(B) – n(A∩B) j
k
(ii) n (A – B) = n (A) – n(A∩B)
(iii) n (B – A) = n(B) – n(A∩B).

(iv) n(A∪B) = n0(A) + n0(B) + n(A∩B)

10 Oasis School Mathematics-10

2. (a) In the given Venn diagram, A and B are the subsets of A BU
the Universal set U. Given numbers represent their cardinal 25 15 30
number. Find:
20
(i) n(A∪B) (ii) n(A∩B) (iii) n(A)

(iv) n(B) (v) n(U) (vi) n( A ∩ B )

(b) In the given Venn diagram, if n(U) = 150, find

(i) n(A∩B) (ii) n0(A) (iii) n0(B) (iv) n(A∪B)
A
BU

80–x x 60–x

40 A BU
x 20 2x
(c) In the given Venn diagram, if n(U) = 60, find the value of
n(A), n(B), n(A∪B) and n(A – B).

3. (a) If n(A) = 12, n(B) = 14, find the maximum value of 25
n(A∪B) and n(A∩B).

(b) If n(A) = 18, n(B) = 16, find the minimum value of n(A∩B) and n(A∪B).

4. (a) If n(A) = 40, n(B) = 60 and n(A∩B) = 10, find the value of n(A∪B).

(b) If n0(A) = 35, n0(B) = 45, n(A∩B) = 20, find (i) n(A) (ii) n(B) (iii) n(A∪B).
5. (a)
'A' and 'B' are the subsets of a universal set U, in which n(U) = 43, n(A) = 25,
n(B) = 18 and n(A∩B) = 7.
(i) Draw a Venn diagram to illustrate the above information.
(b) (ii) Using Venn diagram, find the value of n( A ∪ B ).
If n(A) = 75, n(B) = 85, n ( A ∪ B ) = 15 and n(U) = 130, using a Venn diagram, find
6. (a) the value of (i) n(A∩B) (ii) n0(A) (iii) n0(B).
If n(A) = 40, n(B) = 60 and n(A∪B) = 80, then,

(i) find the value of n(A∩B).

(ii) find the value of n0(A).
(iii) show this in a Venn diagram.

(b) If n(U) = 200, n(M) = 160, n(N) = 150, n( M ∪ N ) = 30, find the value of

(i) n(M∩N) (ii) n0(M) (iii) n0(N)
(iv) Show the above information in a Venn diagram.

7. (a) In a survey of a group of 100 students, 68 passed in Mathematics, 60 passed in
Science, 12 failed in both subjects. Draw a Venn diagram and find the number of
students who

(i) passed in both subjects.

Oasis School Mathematics-10 11

(ii) passed in Mathematics only.
(iii) passed in Science only.

(b) In a survey among 90 people, it was found that 51 people liked to eat oranges and
59 liked to eat apples. If 3 people did not like to eat both the fruits,

(i) how many liked to eat both fruits?
(ii) how many liked to eat only oranges?
(iii) how many liked to eat only apples?
(iv) how many liked to eat only one fruit?
(v) show the above information in a Venn diagram.

8. (a) In a survey of 100 people, it was found that 65 liked folk songs, 55 liked modern
songs and 35 liked folk as well as modern songs.

(i) Draw a Venn diagram to illustrate the fact.

(ii) How many people did not like both songs?

(b) Inasurveyamong350peopleinacommunity,200peopleareinfluencedbymaterialism
and 120 people are influenced by spiritualism. If 120 people are influenced by both,

(i) Show the above information in the Venn diagram.

(ii) Find the number of people who are influenced by neither of them.

9. (a) In a group of 70 people, 37 like tea, 52 like milk and each person likes at least one
of the two drinks.

(i) How many people like both tea and milk ?
(ii) How many people like tea only ?
(iii) How many people like milk only ?

(iv) Show the above information in a Venn diagram.

(b) In a school, all students play either football or volleyball or both. 300 play football,
250 play volleyball and 110 play both the games. Draw a Venn diagram to find:

(i) the number of students playing football only.

(ii) the number of students playing volleyball only.

(iii) the total number of students.

10. (a) In a group of 200 people, 60 like milk only, 50 like curd only and 10 like none of
the two. Using a Venn diagram find the number of people who like both.

(b) In a class of 55 students, 15 liked Maths but not English. 18 students liked English
but not Maths and 5 students did not like both. Find
(i) how many liked both subjects

(ii) how many liked Maths

(iii) how many liked English

(iv) Show this information in Venn diagram.

12 Oasis School Mathematics-10

11. In an election, two candidates P and Q stood for the post and 40,000 people were in
voters list. Voters are supposed to cast the vote for single candidate. 20,000 people
cast vote for P and 15,000 cast for Q and 3,000 people cast vote even for both.

(i) Show these information in Venn diagram

(ii) How many people did not cast their votes?

(iii) How many votes were valid? Find it.

12. (a) In a survey of a group of people, it was found that 39% of the people like tea only,
27% like coffee only and 15% do not like both.

(i) What percentage of the people like both of them?

(ii) What percentage of the people like tea?

(iii) What percentage of the people like coffee?

(iv) Represent the above information in a Venn diagram.

(b) In an examination, 40% of the students passed in Mathematics only and 30%
passed in Science only. If 10% of students failed in both subjects,

(i) what percentage of students passed in both subjects?

(ii) what percentage of students passed in Mathematics?

(iii) represent all the results in a Venn diagram.

13. (a) In a survey of a group of people, it was found that 70% of the people liked Coke,
60% liked Fanta, 2,000 people liked both of them and 20% liked none of them.

(i) Draw a Venn diagram to illustrate the above information

(ii) Find the total number of people in the survey.

(b) In a survey of some students, it was found that 60% of the students studied
Commerce and 40% studied Science. If 40 students studied both the subjects and
10% didn't study any of the subjects, by drawing a Venn diagram,

(i) find the total number of students.

(ii) find the number of students who studied Science only.

14. (a) 32 teachers in a school like either milk or curd or both. The ratio of the number
of teachers who like milk to the number of teachers who like curd is 3:2 and 8
teachers like both milk and curd.

(i) Find the number of teachers who like milk.

(ii) Find the number of teachers who like curd only.

(iii) Represent the above information in a Venn diagram.

Oasis School Mathematics-10 13

(b) In a group of 95 students, the ratio of students who like Mathematics and Science
is 4:5. If 10 of them like both the subjects and 15 of them like none of these subjects,
then by drawing a Venn diagram, find how many of them
(i) like only Mathematics. (ii) like only Science.

(c) Out of the 120 students who appeared in an examination, the number of students
who passed in Mathematics only is twice the number of students who passed in
Science only. If 50 students passed in both subjects and 40 students failed in both
subjects,

(i) find the number of students who passed in Mathematics.

(ii) find the number of students who passed in Science.
(iii) show the result in a Venn diagram.

15. (a) Out of 1500 students who appeared in an examination, 20% students failed in
the examination, 40% of the failures failed in Mathematics only and 20% failures
failed in Science only and 10% failures failed in other subjects. Find

(i) the number of students who failed in both Mathematics and Science.
(ii) show this information in a Venn diagram.

(b) Out of 1000 students who appeared in an examination, 60% passed the
examination. 60% of the failing students failed in Mathematics and 50% of the
failing students failed in English. If the students failed in English and Mathematics
only, find the number of students who failed in both subjects.

Answers
1. Consult your teacher. 2. (a) (i) 70 (ii) 15 (iii) 40 (iv) 45 (v) 90 (vi) 75 (b) (i) 30

(ii) 50 (iii) 30 iv) 110 (c) 25, 30, 35, 5 3. (a) 26,12 (b) 0, 18 4. (a) 90 (b) 55, 65, 100
5. (a) 7 (b) (i) 45 (ii) 30 (iii) 40 6. (a) (i) 20 (ii) 20 (b) (i) 140 (ii) 20 (iii) 10
7. (a) (i) 40 (ii) 28 (iii) 20 (b) (i) 23 (ii) 28 (iii) 36 (iv) 64
8. (a) 15 (b) 150 9. (a) (i) 19 (ii) 18 (iii) 33 (b) (i) 190 (ii) 140 (iii) 440
10. (a) 80 (b) (i) 17 (ii) 32 (iii) 35 11. (i) 8000 (ii) 29,000
12. (a) (i) 19% (ii) 58% (iii) 46% (b) (i) 20% (ii) 60%
13. (a) 4,000 (b) (i) 400 (ii) 120 14. (a) (i) 24 (ii) 8 (b) (i) 30 (ii) 40 (c) (i) 70 (ii) 60
15. (a) 90 (b) 40

Project Work

• Take a class of your school and ask the students whether they like sports,
music, both or none. Collect the information and present it in a Venn
diagram.



14 Oasis School Mathematics-10

Cardinal number of union of three sets: A BU
C
Let A, B and C be three overlapping
subsets of the universal set U.
Hence, cardinal number of A = n(A)
Cardinal number of B = n(B)

Cardinal number of C = n(C)

We have n(A∪B∪C) = n[A∪ (B∪C)] ………… (i)

n[A∩(B∪C)] = n[(A∩B) ∪ (A∩C)] ………… (ii)

n[(A∩B) ∩ (A∩C)] = n(A∩B∩C) ………… (iii)

Now, n(A∪B∪C) = n[A∪(B∪C)] [From (i)]

n [A∪(B∪C)] = n(A) + n(B∪C) – n[A∩(B∪C)]

= n(A) + n(B) + n(C) – n(B∩C) – n[(A∩B) ∪ (A∩C)] [From (ii)]

= n(A) + n(B) + n(C) – n(B∩C) – [n(A∩B) + n(A∩C) – n[(A∩B) ∩ (A∩C)]

= n(A) + n(B) + n(C) –n(B∩C) – n(A∩B) – n(A∩C) + n(A∩B∩C) [From (iii)]

∴ n(A∪B∪C) = n(A) + n(B) + n(C) – n(B∩C) – n(A∩B) – n(A∩C) + n(A∩B∩C)

If A, B and C are disjoint sets, then n(A∪B∪C) = n(A) + n(B) + n(C)

Some important results on cardinality of three sets

n0(A) A BU n0(A∩B)
n0(A∩C) C n0(B)

n0(B∩C)
n(A∪B∪C)

n(A∩B∩C) n0(C)

(i) n(A∪B∪C) = n(A)+n(B)+n(C)–n(A∩B)–n(B∩C)–n(A∩C)+n(A∩B∩C)

(ii) n(A∩B) = n0(A∩B) + n(A∩B∩C)

(iii) n(B∩C) = n0(B∩C) + n(A∩B∩C)

(iv) n(A∩C) = n0(A∩C) + n(A∩B∩C)

(v) n(A) = n0(A) + n0(A∩B) + n0(A∩C) + n(A∩B∩C)

(vi) n(B) = n0(B) + n0(A∩B) + n0(B∩C) + n(A∩B∩C)

(vii) n(C) = n0(C) + n0(A∩C) + n0(B∩C) + n(A∩B∩C)

(viii) n(A∪B∪C) = n0(A)+n0(B)+n0(C)+n0(A∩B)+n0(B∩C)+n0(A∩C)+n(A∩B∩C)

(ix) n(A ∪ B ∪ C) = n(U) – n(A∪B∪C)

Oasis School Mathematics-10 15

Remember !

Verbal form Set notations

* number of elements in either A or B or C n(A∪B∪C)

* number of elements in at least one of A or B or C n(A∪B∪C)

* number of elements in all three sets n(A∩B∩C)

* number of elements in exactly one set n0(A) + n0(B) + n0(C)
* number of elements in exactly two sets n0(A∩B)+n0(B∩C)+n0(A∩C)
* number of elements in none of the sets
n(A ∪ B ∪ C)

Worked Out Examples

Example 1

Sets A, B and C are the subsets of the universal set U. If n(A) = 100, n(B) = 120, n(C) =
110, n(A∩B) = 60, n(B∩C) = 50, n(C∩A) = 55 and n(A∪B∪C) = 200, find n(A∩B∩C) and
illustrate the above information in a Venn diagram.

Solution:

Here, n(A) = 100, n(B) = 120, n(C) = 110, n(A∩B) = 60, n(B∩C) = 50,

n(C∩A) = 55 and n(A∪B∪C) = 200.

We have,

n(A∪B∪C) = n(A) + n(B) + n(C) – n(A∩B) – n(B∩C) – n(C∩A) + n(A∩B∩C)

200 = 100 + 120 + 110 – 60 – 50 – 55 + n(A∩B∩C)

or, 200 = 330 – 165 + n(A∩B∩C)

or, 200 = 165 + n(A∩B∩C)

or, n(A∩B∩C) = 200 –165

or, n(A∩B∩C) = 35

Illustration in Venn diagram Steps

(60 – 35) = 25 Insert n(A∩B∩C) = 35

100 – (25+35+20)=20 U Find n0(A∩B) = n(A∩B) – n(A∩B∩C)
AB = 60–35 = 25
(55–35)=20
120–(25+35+15)=45 Similarly, find n0(B∩C) and n0(A∩C)
n0(A) = 100–25–35–20 = 20
35 (50–35)=15 Similarly, find n0(B) and n0(C)
C

110–(35+15+20)=40

16 Oasis School Mathematics-10

Example 2

In a survey of college students about their interest in movies, the following
information was obtained, 48% like Nepali movies, 40% like English movies, 31%
like Hindi movies, 24% like Nepali and English movies, 19% like Nepali and Hindi
movies, 13% like Hindi and English movies, 6% like all three types of movies. Find:

(i) what percentage of people like none of these movies?

(ii) what percentage of people like only two types of movies?
Solution:

Let N, E and H be the set of students who like Nepali, English and Hindi movies respectively.

Let n(U) = 100

then n(N) = 48, n(E) = 40, n(H) = 31, n(N∩E)= 24

n(N∩H) = 19, n(H∩E) = 13, n(N∩E∩H) = 6

We have, n(N∪E∪H) = n(N) + n(E) + n(H) – n(N∩E)–n(N∩H)–n(E∩H) + n(N∩H∩E)

n(N∪E∪H) = 48 + 40 +31 – 24 – 19 – 13 + 6 = 69

Again, n(N ∪ E ∪ H) = n(U) – n(N∪E∪H) = 100 – 69 = 31

Hence, 31% people like none of these three types of movies.

Again, n0(N∩E) = n(N∩E) – n(N∩E∩H) = 24 – 6 = 18
n0 (E∩H) = n(E∩H) – n(N∩E∩H) = 13–6 =7
n0(N∩H) = n(N∩H) – n(N∩E∩H) = 19–6 = 13
∴ n(only two movies) = 18 + 7 +13 = 38

Hence 38% students like only two types of movies.

Exercise 1.2

1. (a) From the given Venn diagram, find the following. A BU
15 8 12
(i) n0(A) (ii) n0(B) (iii) n0(C)
7
(iv) n0(A∩B) (v) n0(B∩C) (vi) n0(A∩C) 63
7 9C
(vii) n(A∩B∩C) (viii) n(A∪B∪C) (ix) n(U)

(x) n(A) (xi) n(B) (xii) n(C)

(xiii) n(A∩B) (xiv) n(B∩C) (xv) n(A∩C).

(b) In the given Venn diagram, if n(U) = 200, n(P∩Q) = 60, P QU

n(Q∩R) = 52, n(P∩R) = 50, find the values of 25 35

x

(i) n(P∩Q∩R) (ii) n0(P∩Q) 20
(iii) n0(Q∩R) (iv) n0(P∩R)
42 R

Oasis School Mathematics-10 17

(c) Insert the cardinality of the following information in A BU
the Venn diagram and hence find n(U). C

n(A) = 14, n(B) = 10, n(C) = 22, n(A∩B∩C) = 6, n(A∩B)
= 7, n(B∩C) = 9, n(A∩ C) = 11 and n(A ∪ B ∪ C) = 4.

2. (a) If n(A) = 20, n(B) = 40, n(C) = 30, (A∩B) = 10, n(B∩C) = 12, n(A∩C) = 8 and
n(A∩B∩C) = 5, find n(A∪B∪C).

(b) If n(A) = 65, n(B) = 50, n(C) = 35, n(A∩B) = 25, n(B∩C) = 20, n(C∩A) = 15,

n(A∩B∩C) = 5 and n(U)=100, find the value of n(A ∪ B ∪ C) .
(c) If n0(A) = 25, n0(B) = 22, n0(C) = 32, n0(A∩B) = 5, n0(B∩C) = 12, n0(A∩C) = 13,

n(A∩B∩C) = 6 and n(A ∪ B ∪ C) = 15, find n(U).

3. (a) The survey of a group of people shows that 60 like tea, 45 like coffee, 30 like milk,
25 like coffee as well as tea, 20 like tea as well as milk, 15 like coffee as well as
milk and 10 like all three. How many people were asked this question? Solve by
drawing a Venn diagram.

(b) In a class of 175 students, 100 students are studying Maths, 70 Physics, 46
Chemistry, 30 Maths and Physics, 28 Maths and Chemistry, 23 Physics and
Chemistry and 18 all the three subjects.
(i) What percentage of students are studying only one subject?
(ii) What percentage of the students are studying none of these subjects?

(c) In a group of 300 people 50 like oranges only, 60 like apples only, 70 like mangoes
only, 25 like oranges and mangoes but not apple, 30 like oranges and apples but
not mangoes, 35 like mangoes and apple but not oranges. If 15 people do not like
all three, find the number of people who like all three fruits.

4. Out of the total candidates in an examination, 40% students passed in Maths, 45% in
Science and 55% in Health. 10% students passed in Maths and Science, 20% in Science
and Health, 15% in Health and Maths, no one failed in all subjects.

(i) Draw a Venn diagram to show the above information.

(ii) Calculate the percentage of students that passed in all Maths, Science and Health.

5. In a group of students, 30 study English, 35 study Science, 25 study Mathematics,
12 study English only, 15 study Science only, 10 study English and Science only and
6 students study Science and Mathematics only.

(i) Draw a Venn diagram to illustrate the above information.

(ii) Find how many students study all the subjects.

(iii) How many students are there altogether?

18 Oasis School Mathematics-10

Answers
1. (a) (i) 15 (ii) 12 (iii) 9 (iv) 8 (v) 3 (vi) 6 (vii) 7 (viii) 60 (ix) 67 (x) 36 (xi) 30

(xii) 25 (xiii) 15 (xiv) 10 (xv) 13 (b) (i) 42 (ii) 18 (iii) 10 (iv) 8 (c) 29 2. (a) 65 (b) 5
(c) 130 3. (a) 85 (b) (i) 61.71% (ii) 12.57% (c) 15 4. 5% 5. (i) 4, (iii) 62

Project Work
Take a survey in your community among the students studying of the secondary

level in different schools. Ask them about their interest in different sports.
Total number of students in the survey ............................ .
Number of students who like football ............................ .
Number of students who like cricket ............................ .
Number of students who like basketball ............................ .
Number of students who like football and cricket ............................ .
Number of students who like football and basketball ............................ .
Number of students who like cricket and basketball ............................ .
Number of students who like all three games ............................ .
Number of students who like none of these ............................ .
Present these information in a Venn diagram

Miscellaneous Exercise

1. If n(A) = 80, n(B) = 70, n(A∪B) = 100, find n(A∩B). (Ans: 50)

2. If n(P) = 80, n(Q) = 60, n(P∪Q) = 100, using a Venn diagram find the value of

n(P∩Q). (Ans: 40)

3. If n(U) = 300, n0(P) = 90, n0(Q) = 105 and n( P ∪ Q ) = 25, using a Venn diagram find the

value of (i) n(P∩Q) (ii) n(P) (iii) n(Q) [(i) 80 (ii) 170 (iii) 185)]

4. In a class of 40 students, 18 take English, 30 take Mathematics and 3 take neither of
them. How many take both English and Mathematics?

5. In a survey of 120 students, it was found that 17 drink neither tea nor coffee, 88 drink tea

and 26 drink coffee. By drawing a Venn diagram, find out the number of students who

drink both tea and coffee. (Ans: 11)

6. In a music class of 30 students, 15 like guitar, 17 like harmonium and 7 like both of them.

Find the number of students who like neither of them. (Ans: 5)

Oasis School Mathematics-10 19

7. In a survey conducted among 100 students regarding the medium of communication in
an English Boarding School of Kathmandu, it was found that 80 use the English language
and 25 use both English and Nepali languages. If the school allows using English and
Nepali language only, find the number of students using the Nepali language. (Ans: 45)

8. In a survey of a community, it was found that 85% people like the winter season and
65% the summer season. If there were no people who like neither season,

(i) present the above information in a Venn diagram.

(ii) what is the percentage of people who like both the seasons?

(iii) what percentage of the people like the winter season only ? [Ans: 50%, 35%]

9. 40% of the students of a school play football, 30% play volleyball and 20% play both.

If 90 students play neither football nor volleyball, use a Venn diagram and find the

number of students in the school. Also, find the number of students who play only

football. [Ans: 180, 36]

10. In a group of 90 people, 70 like mango, 50 like both mango and orange. Each person
likes at least one of the two fruits. Using a Venn diagram find,

(i) the number of people who like oranges.

(ii) the number of people who like only one fruit. [Ans: (i) 70, (ii) 40]

11. In a group of 150 people, 35 like tea only, 52 like coffee only and 28 like both. Find

(i) how many like none of these?

(ii) Show these information in a Venn diagram [Ans: (i) 35]

12. In an examination, it was found that 55% students failed in Mathematics and 34% failed
in English. If 35% students passed in both subjects,

(i) what percentage of students failed in Mathematics only?
(ii) what percentage of students failed in English only?

(iii) represent the above information in a Venn diagram. [Ans: (i) 31%, (ii) 10%]

13. Out of 60 students of a hostel, 30 like apple, 25 like oranges and the ratio of students
who like apple only and orange only is 5:4, find

(i) how many of them like both of them.

(ii) how many of them like none of them. (Ans: 5, 10)

14. In a group of 100 students, the ratio of students who like Geography and Sociology is
3:5. If 30 of them like both the subjects and 10 of them like none of the subjects, then by
drawing a Venn diagram, find

(i) how many students like Geography only.

(ii) how many students like Sociology only. (Ans: 15, 45)

15. In a survey, one third children like only mangoes and 22 don't like mangoes at all. Also

2/5 children like oranges but 12 like none of them

(i) show the above information in a Venn diagram.

20 Oasis School Mathematics-10

(ii) How many children like both types of fruits? (Ans: 8)

16. In a survey, one third student like only milk and 80 do not like milk. Also 40% like milk
but 40 like none of them.

(i) Show the above data in a Venn diagram.

(ii) How many students like both? (Ans: 20)

17. In a survey, 3 children like only Maths and 70 do not like Maths. 9 like Science but 20
14 14

like none of them,

(i) Show the above data in a Venn diagram.

(ii) How many children like both subjects? (Ans: 40)

18. In an election of municipality, two candidates A and B stood for the post of mayor and
25000 people were in the voter list. Voters were supposed to cast the vote for a single
candidate. 12000 people cost vote for A, 10000 people cost for B and 1000 people cost
vote even for both.

(i) Show these informations in Venn-diagram.

(ii) How many people didn't cost vote?

(iii) How many votes were valid? Find it. (Ans: 4000, 20,000)

19. If n(A) = 48, n(B) = 51, n(C) = 40, n(A∩B) =11, n(B∩C) = 10, n(C∩A) = 9, n(A∩B∩C) = 4

and n(U) = 120, find the value of n(A∪B∪C) and n(A ∪ B ∪ C) . (Ans: 113, 7)

20. In a survey of food taste of a group of people, the following information obtained. 39

like Pizza, 25 like Burger, 22 like Mo:Mo, 20 like Pizza and Burger, 17 like Pizza and

Mo:Mo, 9 like Burger and Mo:Mo, 4 like all three and 6 like none of these. Find the

number of people in the survey. (Ans: 50)

21. In a survey of students, it was found that 50% of them liked English, 60% liked
Mathematics and 40% liked Science. If 20% liked Maths and English, 15% liked English
and Science, 25% liked Maths and Science and 5% liked all these three subjects, with the
help of a Venn diagram, find

(i) what percentage of students like only two subjects?

(ii) what percentage of students don't like any subject? (Ans: 45%, 5%)

22. In a group of 60 people, 5 did not like any of tea, coffee and milk. If the ratio of people

who like only one, only two and all three is 6:3:2, find the number of people who like

only one. (Ans: 30)

23. Among the examinees of a school in Kathmandu, 40% students in Science, 45% in Maths
and 55% in English obtained A+ grades. Similarly, 10% in Maths and Science, 20% in
Science and English and 15% in English and Maths obtained A+ grade. If every student
obtained an A+ grade in at least one subject,

(i) show the above information in a Venn diagram.

(ii) find the percentage of students who obtained an A+ grade in all three subjects.

(iii) If 300 students were surveyed, how many students obtained an A+ in only

one subject? (Ans: 65%, 195)

Oasis School Mathematics-10 21

Attempt all the questions. Full marks: 20
[4 × 5 = 20]

1. If n(A) = 40, n(B) = 60, n(A∩B) = 30, n(U) = 100, find n n(A∪B) using a Venn diagram.

2. Among the students who appeared in an examination, 75% passed in English, 80%
passed in Science and 70% passed in both subjects. Using a Venn diagram, find the total
number of students if 750 students failed in both subjects.

3. In a group of 150 students, the ratio of number of students who like Nepali to the number
of students who like English is 3:5. If 50 students like both and 40 do not like both, find
the number of students who like (i) Nepali only (ii) English only.

4. If n(A) = 50, n(B) = 40, n(C) = 60, n(A∩B) = 30, n(B∩C) = 25, n(A∩C) = 20,
n(A∩B∩C) = 15, and n(∪) = 150, find n(A∪B∪C) and n (A∪B∪C) .

5. In a Survey of 200 students, every student study at least and of the three subjects Maths,
English or Science. If the number of students who study only one subject is twice the
number of students who study only two subjects and 10%. Study all three, find the
number of students who study only one subject.



22 Oasis School Mathematics-10

Arithmetic

20Estimated Teaching Hours

Contents

• Tax
• Money Exchange
• Compound Interest
• Population Growth
• Depreciation

Expected Learning Outcomes

At the end of this unit, students will be able to develop the following
competencies:

• To collect and solve problems related to the value added tax
in our daily life

• To convert foreign currency into Nepali currency and
Nepali currency into foreign currency from the given rate of
exchange.

• To calculate the CI compounded annually upto 3 years
• To calculate the CI compounded semi-annually upto 2 years
• To solve the problems of population growth and deprecation

Materials Required

• Bill, exchange rates, chart paper, A4 size paper, sketch pen

Oasis School Mathematics-10 23

Unit Tax and Money
Exchange
2

2.1 Warm-up Activities

Discuss the following in your class and draw the conclusion.

• The marked price of an article is Rs. 650. If it is sold at Rs. 500, what is the amount of
discount? What is the discount percentage?

• The marked price of an article is Rs. 1,200. If 20% discount is allowed, how much does a
costumer have to pay?

• An article is sold at Rs. 500 after a discount of 10%. What is the marked price of the
article?

• A man gets a discount of Rs. 500 on an article which is marked Rs. 2,000. Find the rate of
discount.

2.2 Value Added Tax

VAT is a tax which we pay when we buy either goods or services. It is always imposed
on the selling price.

VAT rates are different in different countries.

The present VAT rate in Nepal is 13%.

Smriti bought a laptop at the discount of 20% which was marked Rs. 30,000.
How much did she pay?

Here, discount = 20% of Rs. 30,000

20
= 100 × Rs. 30,000

= Rs. 6,000

Now, selling price Rs. 30,000 – Rs.6,000 = Rs. 24,000. But her bill is Rs. 27,120.

She paid Rs. 27,120.

Why did she pay Rs. 3,120 more than the selling price?

The extra amount Rs. 3,120 paid by Smriti is the Value Added Tax (VAT). It is always
calculated on the S.P.

24 Oasis School Mathematics-10

Let's compare these two bills.

ABC Store XYZ Store

Birtamod, Jhapa Ghorahi, Dang
Date: 2073/9/5
Date: 2073/9/2
Name................R..e..w...a...P...o..k..h..r..e..l.................... Name............K...a..u..s..h..a..l...P..a..n..d...e..y....................

S.N. Items Qty. Rate Price S.N. Items Qty. Rate Price

1. Watch 1 12,000/- 12,000/- 1. Laptop 1 28,000/- 28,000/-

2. Mobile Set 1 18,000/- 18,000/- 2. Mobile Set 1 22,000/- 22,000/-

Total 30,000/- Total 1 50,000/- 50,000/-
Discount 10%
Grand Total 3,000/- Discount 20% 10,000/-
27,000/- Sub-total 40,000/-
VAT 13% 5,200/-

Grand Total 45,200/-

• What is the rate of discount in the first bill?
• What is the rate of discount in the second bill?
• What extra amount has been added in the second bill?
• What is that additional amount called?
• What is the rate of that extra amount?
• What is the difference between these two bills?

S.P. including VAT

The price paid by the buyer (customer) for an article, including the VAT over the S.P., is
called the net S.P. or S.P. including VAT or actual S.P. This is the final price a buyer has
to pay.

Hence, mathematically we can write: M.P– Discount

– L+oPsrsofit S.P. + VAT
Net S.P. = S.P. + VAT
i.e. S.P. with VAT = S.P. + VAT


We can relate the terms C.P., S.P., Profit,

Loss, M.P., Discount, VAT and S.P. with

VAT as shown in the adjacent figure.

S.P. with
C.P. VAT

Oasis School Mathematics-10 25

Remember !

Discount = Discount % of M.P.
=
S.P. = M.P. – Discount
=
= M.P. – Discount % of M.P.
=
VAT VAT % of S.P.
=
SP with VAT S.P. + VAT

Net S.P. S.P. + VAT % of SP

Discount percent Discount × 100% = M.P.–S.P × 100%
M.P. M.P.

VAT percent = VAT× 100% = Net S.P–S.P
S.P. S.P. × 100%

• VAT is added on the price after adding insurance, transportation charge, local taxes
profit and deducting discount.

Cost price
Add profit, insurance, local taxes and transportation charge

Marked price
Subtract discount

Selling price
Add VAT

Selling price
with VAT

Worked Out Examples

Example: 1

A customer paid 13% VAT on the selling price Alternative method
of Rs. 150. How much did he pay for the
article? S.P. with VAT = S.P. + VAT% of S.P
Solution:
S.P. of article = Rs. 150 = 150+13% of 150
= 150 + 11030× 150
VAT = 13% of S.P. = 150 + 19.50

= 13 × Rs. 150 = Rs. 169.50
100

26 Oasis School Mathematics-10

195
= Rs. 100 = Rs.19.50

∴ S.P. with VAT = S.P. + VAT

= Rs. 150 + Rs.19.50

= Rs. 169.50
Example : 2

A man paid Rs. 3390 for an article after levying 13% VAT. Find the selling price of the
article.

Solution: Alternative method

Here, S.P. with VAT = Rs. 3390 Let S.P. = x

VAT % = 13% VAT% = 13%

S.P. = ? wiV3t3hA9TV0A==T11131=0%30xxo+f11x103=0x1130x0
S.P.
We have,

S.P. with VAT = S.P. + VAT% of S.P.

3390 = S.P. + 13% of S.P.

or, 3390 = S.P. + 13 × S.P. or, x = 3390×100 = 3000
100 113

or, 3390 = 113 S.P ∴ S.P. = Rs. 3000.
100

or, 3390 × 100 = 113 S.P.

or, S.P. = 3390 ×100
113

∴ S.P. = Rs. 3000.

Example : 3

The M.P. of a sweater is Rs. 1500. Find the Net S.P. after allowing 20% discount and
then adding 13% VAT.

Solution:

Here, M.P. = Rs. 1500

Discount = 20% of Rs.1500 = 20 × Rs. 1500 = Rs.300
100

∴ S.P. after discount = Rs. 1500 – Rs. 300

= Rs. 1200

No w, VAT = 13% of S.P.

= 13 × Rs. 1200 = Rs. 156
100

Net S.P. = Rs. 1200 + Rs. 156 = Rs. 1356

Oasis School Mathematics-10 27

Example: 4

After allowing a discount of 20%, an article is sold for Rs. 1808 including 13% VAT.
Find its original price.
Solution:

Let the original price (M.P.) = Rs. x

Now, Discount = 20% of M.P = 20 ×x= x
100 5

S.P. = M.P. – Discount Alternative method

= x– x 5x – x = 4x Given, discount % = 20%
5 =5 5 S.P. with VAT = Rs. 1808
VAT% = 13%
Further, 4x 4x
5 5 We have,
S.P. including VAT = + 13% of

= 4x + 13 × 4x = 4x + 13x S.P with VAT = S.P+VAT% S.P.
5 100 5 5 125
1808 = S.P. + 13 × S.P.
100x + 13x 100
125
= or, 1808 = 113SP
100

113x or S.P. = 1808×100
By the question: = 125 113

or, S.P. = Rs. 6 × 100

113x = 1,808 or, S.P. = Rs. 16 × 100
125
= Rs. 1600
Again,
1808 ×125
∴ x = 113 S.P. = M.P. – D% of M.P.

= Rs. 2000 1600 = M.P. – 20% of M.P.
∴ Original pri ce = Rs. 2000.
1600 = M.P. – 20 × M.P.
100

1600 = 80M.P.
100

M.P. = 1600 × 100 = Rs. 2000
80

∴Original price = Rs. 2000.

Example: 5
After allowing 16% discount on the marked price of an article and levying 13% value
added tax, the price of the article becomes Rs. 9,492.

(i) Find the marked price. (ii) Find the amount of VAT.
Solution:

Let, Marked price (M.P.) = Rs. x

We have, S.P. = M.P. – Discount % of M.P.

28 Oasis School Mathematics-10

= x – 16% of x

= x – 16 ×x
100

= x– 4x
25

21x
= 25

Again, S .P. with VAT = S. P. + VAT % of S. P.

= 21x + 13 × 21x
25 100 25

21x 273x
= 25 + 2500 Alternative method

= 2100x + 27 3 x S.P. with VAT = Rs. 9492
2500 VAT% = 13%
2373x
= We have, S .P. with VAT = S.P. + VAT% of S.P.
= 2500
Now, 2373x = 9,492 or, 9492 = SP + 13 × SP
2500 = 100

9492 × 250 0 or, 9492 = 113 SP
2373 or, S.P. =
or, x 100 × 1 00
9492
= Rs. 8400
113
or, x 4 × 2,500
Discount = 16%

or, x = 10,000 We have, 8400 = M.P. – 16 × M.P.
100

∴ Marked Price = Rs. 10,000 84MP
Again, amount of VAT = VAT % of S. P. 8400 = 100

21x M.P. = Rs. 10,000
= 13% of 25 VAT = VAT% of S.P.
Again,

= 13 × 21×215000 0 = 13% of 8,400
100 =
13
= 13 × 21 × 4 = 1 092 100 × 8,400

∴ Amount of VAT = Rs. 1092 = Rs. 1,092

Example: 6

The marked price of an article is Rs. 4,500. After allowing a certain percent of discount
and with 13% VAT levied, the article is sold at Rs. 4068. Find the discount percentage.
Solution:

Given, S.P. with VAT = Rs. 4068

VAT = 13%

Oasis School Mathematics-10 29

We have, S.P. with VAT = S.P. + VAT % of S.P.

or, 4,068 = SP + 13 × SP
or, 100

113 SP
4,068 = 100

or, S.P. = 4068 ×100
113

or, S.P. = 36 × 100

∴ S.P. = Rs. 3,600

Again, M.P. = Rs. 4,500

S.P. = Rs. 3,600

Discount = M.P. – S.P.

= Rs. 4,500 – Rs. 3,600

= Rs. 900

We have, Discount × 100%
Discount percent = M.P.

= 900 × 100% = 20%
4500

Example : 7

A sold a machine to B at Rs 11,000 excluding VAT. B sold this same machine to C with
a profit of Rs. 2000, adding Rs. 500 local tax and Rs. 1200 transportation charge. Find
the amount of VAT that C has to pay to B, if the rate of VAT is 13%. Also find how
much VAT amount does B get back?

Solution:

Here, Cost price paid by B = Selling price received by A excluding VAT

= Rs. 11,000

Net C.P. paid by B = Rs. 11,000 + local tax + transportation charge

= Rs. 11,000 + Rs. 500 + Rs. 1,200

= Rs. 12,700

While selling it to C,

Selling price (S.P.) = Rs. 12,700 + Profit

= Rs. 12,700 + Rs. 2,000

= Rs. 14,700

∴ VAT applicable amount for C = 14,700

VAT amount to be paid by C = 13% of 14,700

= 13 × Rs. 14,700 = Rs. 1,911
100

30 Oasis School Mathematics-10

Again, VAT amount to be returned back to B = 13% of 11,000

= 13 × 11,000
100

= Rs. 1430

Example : 8

A man bought a machine for Rs. 20,000. He paid Rs. 800 transportation charge,
Rs. 1200 local tax and wants to make a profit of Rs. 2,000. Find (i) marked price

(ii) selling price if 5% discount is given, (iii) VAT amount if 13% VAT is added.

Solution:

Here, cost price of the machine (C.P.) = Rs. 20,000.

Here, Net C.P. = Rs. (20,000 + 800 + 1,200 + 2,000) = Rs. 24,000

(i) While selling it to customer, M.P. = Rs. 24,000

(ii) Discount = 5% of 24,000

= 5 × 2,4000 = Rs. 1200
100

∴ Selling price (S.P.) = Rs. 24,000 – Rs. 1,200 = Rs. 22,800

(iii) VAT amount = VAT % of S.P.

= 13% of 22,800

= 13 × 22,800 = Rs. 2,964
100

Exercise 2.1

1. (a) What is the current VAT rate of Nepal?
(b) If discount percentage and marked price are given, write the formula to calculate

the discount.
(c) If marked price (M.P.) and selling price (S.P.) are given, write the formula to

calculate the discount.
(d) If discount and marked price are given, write the formula to calculate the discount

percentage.
(e) If VAT rate and S.P. are given, write the formula to calculate the VAT.
(f) If net S.P. and S.P. are given, write the formula to calculate the VAT amount.
(g) If S.P. and VAT rate are given, write the formula to calculate the net S.P.
(h) If VAT and S.P. are given, write the formula to calculate the VAT percentage.

Oasis School Mathematics-10 31

2. Find the VAT and percentage of VAT in each of the following cases.
(a) S.P. = Rs. 1,400, S.P. with VAT = Rs. 1,582
(b) S.P. = Rs. 1,550, S.P. with VAT = Rs. 1,705
3. (a) If S.P. = Rs. 1,500, VAT % = 13%, find S.P. with VAT.
(b) If S.P. = Rs. 22,500, VAT % = 13%, find S.P. with VAT.
(c) If S.P. with VAT = Rs. 1,130, VAT % = 13%, find S.P.
(d) If S.P. with VAT = Rs. 1,650, VAT % = 10%, find S.P.

4. (a) The selling price of one plate Mo:Mo is Rs. 80. Find the net selling price if 13% VAT
is imposed.

(b) 15% VAT is included on the selling price of a jacket. If the selling price is Rs. 1000,
find its net selling price.

(c) Sandesh paid Rs. 175 for a calculator including VAT, which originally cost Rs. 150.
Find the VAT and its percentage.

(d) The net S.P. including 12.5% VAT for a Nepali handicraft is Rs. 225. Find its original
selling price.

(e) Pushpa paid Rs. 5,650 for a mobile set including 13% VAT. Find its actual price.

5. (a) The marked price of a radio is Rs. 5,000. What will be the price of the radio if 10%
VAT is levied, after allowing 15% discount on it?

(b) The marked price of one set of computer is Rs. 65,500. What will be the price of the
computer if 15% value added tax is levied after allowing 12% discount on it?

(c) The marked price of a motorcycle is Rs. 85,000. What will be the price of the
motorcycle if 18% VAT is levied after allowing 15% discount on it?

6. (a) If a tourist paid Rs. 5,610 for a carved window made out of wood with a discount
of 15% including 10% VAT,

(i) what is the marked price of the window?
(ii) what is the amount of discount?
(iii) what is the amount of VAT?
(b) After allowing 15% discount on the marked price of a TV set, 10% VAT was levied

on it. If the TV set was sold for Rs. 22,440, calculate the marked price.
(c) A machine is sold at Rs. 99,000 after 10% discount and levying 10% VAT. Find the

discount and VAT amount.
(d) After allowing 15% discount on the marked price of an article and 13% VAT was

levied on it, the price of the article was fixed at Rs. 4,610.40. What was the amount
of VAT levied?
7. (a) After allowing 20% discount on the marked price and then levying 10% VAT, a
radio was sold. If the buyer had paid Rs. 320 as VAT, find the amount of discount.

32 Oasis School Mathematics-10

(b) A shopkeeper gives 20% discount on the marked price of a television set. The VAT
amount at the rate of 13% is Rs. 2,600. Find the marked price and the amount of
discount.

(c) A shopkeeper allows 20% discount on the marked price of an article and 13% VAT
is levied upon it. If the customer pays Rs. 468 as VAT, find the amount of discount.
Also find by how much percent discount is more than VAT?

8. (a) After allowing 15% discount on the marked price and levying 10% VAT, an article
is sold. If the customer gets a discount of Rs. 600, find the VAT amount.

(b) A customer gets a discount of Rs. 1,500 at a rate of 10%. If 13% VAT is added, find
the amount of VAT paid by the customer.

9. (a) After allowing 15% discount, a man paid a VAT of Rs. 442 on the selling price. Find
the VAT percentage if the marked price is Rs. 4,000.

(b) The marked price of an article is Rs. 460. A discount of 5% is offered on it. If a
customer paid Rs. 43.70 as VAT, find the percentage of VAT.

10. (a) The marked price of an article is Rs. 3,200. If discount is allowed and the customer
buys it for Rs. 2,640 including 10% VAT, what is the discount percentage?

(b) Marked price of an article is Rs. 3760. After allowing certain percent of discount
and adding 15% VAT on it, its price becomes Rs. 4107.80. Find the rate of discount.

11. (a) A dealer sold a laptop to a retailer for Rs. 40,000 excluding VAT. The retailer sold
it at a profit of Rs. 5,000. If the retailer paid Rs 1,500 as local tax before he sold it to
the customer, find

(i) how much the customer paid as VAT?
(ii) how much money the customer paid for the laptop? (Given that VAT rate is 13%).
(iii) how much VAT amount does the retailer get back?

(b) A dealer sold a machine to a retailer at Rs. 1,20,000 excluding VAT. The retailer
sold it at a profit of 10% after adding transportation charge Rs. 10,000 and paying
local tax Rs. 3,000. If VAT rate is 13%, find

(i) the amount of VAT that a customer has to pay while buying it from the retailer.
(ii) the total amount that a customer has to pay.
(iii) how much VAT amount does the retailer get back?

(c) Supplier 'A' sold some construction materials of Rs. 2,00,000 to supplier 'B' making
20% profit and adding 13% VAT. Supplier B spent Rs. 6,000 for transportation
charge and made 10% profit to the purchased price excluding VAT and levied
local tax Rs. 5,000 and sold to contractor. Find the VAT amount to be paid by
contractor.

12. (a) A man bought a machine for Rs. 80,000. He paid Rs. 5,000 in transportation
charges, Rs. 2,500 in local taxes and wants to make a profit of Rs. 11,500. Find

(i) the marked price of the machine.

(ii) selling price if 10% discount is given.

(iii) amount of VAT that should be paid by the customer if 13% VAT is added.

Oasis School Mathematics-10 33

(b) A photocopy machine is bought by a retailer for Rs. 90,000. He paid a Rs. 6,000
transportation charge and Rs. 3,000 local tax. If he wants to make a profit of Rs.
12,000, find

(i) the marked price of the photocopy machine.

(ii) selling price if 5% discount is given.

(iii) VAT, if the rate of VAT is 13%.
(iv) total amount paid by the customer.

Answers
1. Consult your teacher 2. (a) Rs. 182, 13% (b) Rs. 155, 10% 3. (a) Rs. 1,695
(b) Rs. 25, 425 (c) Rs. 1,000 (d) Rs. 1,500
4. (a) Rs. 90.40 (b) Rs. 1,150 (c) Rs. 25, 16.67% (d) Rs. 200 (e) Rs. 5,000
5. (a) Rs. 4,675 (b) Rs. 66,286 (c) Rs. 85,255
6. (a) (i) Rs. 6000 (ii) Rs. 900 (iii) Rs. 510 (b) Rs. 24,000 (c) Rs. 10,000, Rs. 9000 (d) Rs. 530.40
7. (a) Rs. 800 (b) Rs. 25,000, Rs. 5000 (c) Rs. 900 8. (a) Rs. 340 (b) Rs. 1755
9. (a) 13% (b) 10% 10. (a) 25% (b) 5% 11. (a) (i) Rs. 5975, (ii) Rs. 67800, (iii) Rs. 5200,
(b) (i) Rs. 19019 (ii) Rs. 1,65,319, (iii) Rs. 15,600 (c) Rs. 35750 12. (a) (i) Rs.99,000 (ii) Rs. 89,100

(iii) Rs. 11,583 (b) (i) Rs. 1,11,000 (ii) Rs. 1,05,450, (iii) Rs. 13,708.50 (iv) 1,19,158.50

Project Work

Visit the tax office and list the articles on which VAT is imposed and VAT is not imposed.

2.3 Money Exchange

• Gaurav's father works in the USA. He sent 10,000 U.S. Dollars to Nepal. How to convert
10,000 U.S. Dollars into Nepali currency ?

• Dawa has to go to Europe. He needs some Euros. How do you convert Nepali currency
into Euros?

• Sundar works in Qatar. He sent 5000 Qatari Riyal to his family. How much Nepali
Rupees does his wife receive ?

There are many such examples in our daily life related to money.
Every country has its own currency. It has its own value. The value of different currencies

is different, like Rs. 100 I.C. is equal to Rs. 160 N.C. In our country, Nepal Rastra Bank
determines the conversion rate of different currencies into Nepali currency. The given
table shows the rate of exchange for Poush 13, 2073.

34 Oasis School Mathematics-10

Exchange Rate fixed by Nepal Rastra Bank

Currency Unit Buying rates (Rs) Selling Rate (Rs)

Indian Rupees 100 160.00 160.15

Open Market Exchange Rates

(for the purpose of Nepal Rastra Bank)

Currency Unit Buying rates (Rs) Selling Rate (Rs)

U.S. Dollar 1 108.18 108.78

European Euro 1 113.00 113.63

UK Pound Sterling 1 132.91 133.65

Swiss Franc 1 105.39 105.97

Australian Dollar 1 77.90 78.33

Canadin Dollar 1 80.11 80.55

Singapore Dollar 1 74.75 75.16

Japanese Yen 10 9.24 9.29

Chinese Yuan 1 15.57 15.66

Saudi Arabian Riyal 1 28.84 29.00

Qatari Riyal 1 29.71 29.87

Thai Baht 1 3.01 3.02

UAE Dirham 1 29.46 29.62

Malaysian Ringgit 1 24.18 24.31

South Korean Won 100 9.00 9.05

Swedish Kroner 1 11.72 11.79

Danish Kroner 1 15.20 15.29

Hong Kong Dollar 1 13.94 14.02

Kuwaity Dinar 1 353.41 355.37

Baharain Dinar 1 286.91 288.50

Note :
• Under the present system, the open market exchange rates quoted by different banks

may differ.

• Use buying rate while converting other currencies into Nepali currency and use selling
rate while converting Nepali currency into other currencies.

Worked Out Examples

Example: 1
Using the above rate of exchange, convert $ 125 into Nepali rupees.
Solution:

Using the buying rate ,

$1 = Rs. 108.18
∴ $125 = Rs.125 × 108.18

= Rs. 2,704.50

Oasis School Mathematics-10 35

Example: 2

Using the above table, convert the following currencies into Nepali rupees.

a. 1500 Qatari riyal b. £ 250 c. 3,250 Euro

d. 8,500 South Korean Won e. 50,000 Japanese yen.

Solution :

a. Using buying rate, b. Using buying rate,

1 Qatari riyal = Rs. 29.71 1 Pound Sterling = Rs. 132.91

then, then, 250 Pound Sterling = Rs. 250 × 132.91

1500 Qatari riyal = Rs. 1,500 × 29.71 = Rs. 33,227.50

= Rs. 44,565

c. Using the buying rate, d. Using buying rate,

1 Euro = Rs. 113 100 South Korean won= Rs. 9

then, 1 South Korean won = Rs. 9
100
9
250 Euros = Rs. 113 × 3250 8500 South Korean won = Rs. 100 × 8,500

= Rs. 3,67,250 = Rs. 765

e. Using the buying rate,

10 Japanese yen = Rs. 9.24

1 Japanese yen = Rs. 9.24
10

50,000 Japanese yen = Rs. 9.24 × 50,000
10

= Rs. 46,200

Example: 3
Using the buying rate, convert 50 U.S. Dollars into Japanese yen.

Solution:

First, let's convert 50 U.S. Dollars into Nepali rupees.

From the above table, 1 U.S. Dollar = Rs. 108.18 Alternative method

then, 50 U.S. Dollars = Rs. 50 × 108.18 = Rs. 5409. Let, $ 50 = x Yen

Again, convert Nepali Rupees into Japanese Yen 10 Yen = Rs. 9.24

Now, Rs. 9.24 = 10 Japanese Yen Rs. 108.18 = $ 1

Re 1 10 Using chain rule,
= 9.24 Japanese Yen
50 × 10 × 108.18 = x × 9.24

10 or, x = 50×10×108.18 = 5853.90 Yen
Rs. 5409 = 9.24 × 5409 Japanese Yen 9.24

= 5853.90 Japanese Yen ∴ $ 50 = 5853.90 Yen

36 Oasis School Mathematics-10

Example: 4
Using the above rate, convert 1 Euro into South Korean won. (Use buying rate)
Solution :

From the above table,

1 Euro = Rs. 113

Let's convert Rs. 113 into South Korean won.

Rs. 9 = 100 South Korean won

Re 1 = 100 South Korean won.
Rs. 113 9

= 100 × 113 South Korean won
9

Rs. 113 = 1255.56 south Korean won

∴ 1 Euro = 1,255.56 South Korean won.

Example : 5
A man needed 6,000 U.S. Dollars. While converting Nepali currency into Dollars, the

bank took a commission of 1%, find how much Nepali currency he needs.
Solution :

Let's convert 6,000 U.S. Dollars into Nepali rupees.

Here, 1 U.S. Dollar = Rs. 108.18

then, 6,000 U.S. Dollars = Rs. 108.18 × 6000

= Rs. 6,49,080

Now, commission = 1% of Rs. 6,49,080
1

= 100 × Rs. 6,49,080

= Rs. 6490.80

∴Total money required = Rs. 6,49,080 + Rs. 6,490.80

= Rs. 6,55,570.80.

Example: 6
Himanka converted Rs. 6,00,000 into Pound Sterling. After one week, Nepali rupees

got devalued by 5%, find whether he has made a profit or loss.
(Given 1 Pound Sterling = Rs. 132.91)

Solution :

1 Pound Sterling = Rs. 132.91

i.e., Rs. 132.94 = 1 Pound Sterling
1

Re. 1 = 132.91 Pound Sterling

Oasis School Mathematics-10 37

Rs. 6,00,000 = 1 × 6,00,000 Pound Sterling
132.91

= 4514.33 Pound Sterling

After the devaluation of the Nepali rupees,

1 Pound Sterling = Rs. 132.91 + 5% of Rs. 132.91 = Rs. (132.91 + 5 × 132.91)
100

= Rs. 139.56

Now, 1 Pound Sterling = Rs. 139.56

4,514.33 Pound Sterling = Rs. 139.56 × 4514.33

= Rs. 629,999.58

His profit = Rs. 629,999.58 – Rs. 6,00,000

= Rs. 29,999.58

Example: 7
A machine is bought from the Indian market at Rs. 64,000 I.C. Find its cost in the

Nepali market if 50% customs duty and 13% VAT are added.

Solution:

Cost of the machine = Rs. 64,000 I.C.

Since, Rs. 100 I.C. = Rs. 160 N.C.

160
Re 1 I.C. = Rs. 100 N.C.

160
Rs. 64,000 I.C. = Rs. 100 × 64,000

= Rs. 102,400

Now, customs duty = 50% of Rs. 1,02,400

= Rs.50 × 1,02,400 = Rs. 51,200
100

Cost of the machine in N.C. = Rs. 1,02,400 + Rs. 51,200 = Rs. 1,53,600

VAT = 13% of Rs. 1,53,600

= Rs.13 × 1,53,600
100

= Rs. 19,968

∴ S.P. with VAT = Rs. (1,53,600+19,968)

= Rs. 1,73,568.

Example : 8
Kumar bought 500 Nepali Thanka scrolls at Rs. 1500 per piece. At what rate can he

sell it in the Chinese market to make a profit of 80%, if he paid 5% export tax?
Solution:

38 Oasis School Mathematics-10

Cost of a piece of Thanka = Rs. 1,500

Cost of 500 Thanka pieces = Rs. 1,500 × 500

= Rs. 7,50,000

Export tax = 5% of Rs. 7,50,000

Rs.5
= 100 × 7,50,000 = Rs. 37,500
∴ Total cost including export tax = Rs. 7,50,000 + Rs. 37,500

= Rs. 7,87,500

Profit % = 80%

Selling price = Rs. 7,87,500 + 80% of Rs. 7,87,500

= Rs. 7,87,500 + 80 × 7,87,500
100

= Rs. 7,87,500 + Rs. 6,30,000

= Rs. 14,17,500

Let's convert Rs. 14,17,500 into Chinese yuan

From the above table,

1 Chinese yuan = Rs. 15.57

i.e. Rs. 15.57 = 1 Chinese yuan

Re. 1 = 1 × Chinese yuan
15.57
1
Rs. 14,17,500 = 15.57 × 14,17,500 Chinese yuan

= 91,040.46 Chinese yuan.

S.P. of 500 Thanka = 91,040.46 Chinese yuan

S.P. of 1 Thanka = 91040.46 Chinese yuan
500

= 182.08 Chinese yuan

∴ He can sell it for 182.08 Chinese yuan per Thanka.

Example : 9

A man converted Rs. 6,50,000 to Euro for his Europe tour at the rate of 1 Euro =
Rs. 130. During his stay in Europe he spent 4500 Euro. Before his arrival in Nepal
Nepali currency is devaluated by 2%, find how much Nepali rupees is left with him.

Solution:

Given, 1 Euro = Rs. 130

Re 1 = 1 Euro
130

Rs. 6,50,000 = 1 × 6,50,000 Euro = 5000 Euro.
130

Oasis School Mathematics-10 39

Since he spent 4500 Euro on his Europe tour

Money left with him = 5000 Euro – 4500 Euro

= 500 Euro

Again, Nepali currency is devaluated by 2%,

New rate of exchange

1 Euro = Rs. (130 + 2% of 130)

= Rs. (130 + 2 × 130) = Rs. 132.50.
100

Now, converting 500 Euro into Rupees,

500 Euro = Rs. 500 × 132.60

= Rs. 66,300

Exercise 2.2

1. (a) If 1 U.S. Dollar = Rs. 108.18, convert 150 U.S. Dollars into rupees.

(b) If 1 Pound Sterling = Rs. 132.91, convert 250 Pound Sterling into rupees.

(c) If 1 Euro = Rs. 113, convert 425 Euro into rupees.

(d) If 1 Qatari riyal = Rs. 29.71, convert 500 Qatari riyal into rupees.

(e) If Rs. 100 I.C. = Rs. 160 N.C., convert Rs. 10,600 I.C. into N.C. rupees.

2. (a) Using the above table and applying the buying rate convert Rs. 60,000 into

i. U.S. Dollars ii. Euro iii. Indian rupees

iv. Pound Sterling v. Chinese yuan vi. Thai baht

(b) Using the above table and applying the selling rate, convert Rs. 25,000 into

i. Japanese yen ii. Singapore Dollar iii. Canadian Dollar

iv. UAE dirham v. Swiss franc Currency Unit Buying/Rs. Selling/Rs.
3. (a) Using the table given alongside convert:
i. 6500 Thai baht into U.S. Dollar. Indian Rupees 100 160.00 160.15
ii. 3000 sterling pound into Japanese yen
iii. 450 Australian Dollar into Indian U.S. Dollar 1 108.36 108.96

rupees European Euro 1 113.87 114.50
iv. 1200 Chinese yuan into Euro
UK Pound Sterling 1 133.11 133.85
(Use buying rate only)
Australian Dollar 1 79.01 79.45

Japanese Yen 10 9.29 9.34

Chinese Yuan 1 15.74 15.83

Thai Baht 1 3.03 3.05

(b) Use the selling rate of the table given above to convert:

i. £1 into U.S. Dollars.

ii. 1 Euro into Chinese yuan

iii. 75 U.S. Dollars into Japanese yen

iv 350 Australian Dollars into Indian rupees.

4. (a) According to exchange rate of Nepal Rastra Bank, the laying and selling rates of $ 1

are Rs. 110.50 and Rs. 111.30 respectively. If a man bought $ 6,000 and sold it, find his

profit.

40 Oasis School Mathematics-10

(b) The buying rate and selling rate of £1 are Rs. 132.50 and Rs. 133.80 respectively. If
£8,000 is bought and sold by money exchange centre, what is the profit in rupees.

(c) According to the exchange rate of Nepal Rastra Bank, the buying rate and selling rate
of 1 Euro is equal to Rs. 113.87 and Rs. 114.50, find

(i) how much Euros can be exchanged with Rs. 40,000?
(ii) how much Nepali rupees can be exchanged with 6,000 Euros?
(d) Selling rate of 1 Australian Dollar is equal to Rs. 80.65. A bank bought 6,000

Australian Dollar and made a profit of Rs. 4,200. Find the buying rate of Australian
Dollar.
5. (a) If 1 US Dollar = Rs. 108.35 and £1 = Rs. 132.65, convert 500 US Dollar into Pound
sterling.
(b) If Rs. 100 NC = Rs. 160 IC and 1 Chinese Yuan = Rs. 15.60, NC find the exchange rate
of Chinrse Yuan and Indian Rupees.
6. (a) 1 American dollar = Rs. 110. If Nepali currency is devaluated by 5%, find the new rae
of exchange.
(b) 1 Euro = Rs. 118. If Nepali currency is devaluated by 2%, find new rate of exchange.
Using new rate of exchange convert 200 Euro into Nepali currency.
(c) Given that £1 = Rs. 140. If Nepali currency is devaluated 2%, find (i) new rate of
exchange. Using new rate convert £50 into Nepali currency and convert Rs. 60,000
into sterling Pound.
7. (a) Abdul works in a gas station in the US. He earns $ 25.6 per hour.
i. Convert his income per hour into rupees.
ii. If he works 9 hours a day, find his daily income in rupees. (Given $1 = Rs. 105.15)
(b) Sonam works in a departmental store in Malaysiya. He makes 30 ringgit per hour. If
1 Malaysian ringgit = Rs. 24.18,
i. find his hourly income in rupees.
ii. find his daily income in rupees if he works 10 hours per day.
iii. find his monthly income.
(c) Aadhya works in a bank in the UK. She gets £ 45 per hour. Find
i. her income per hour in rupees.
ii. her daily income in rupees if she works 7 hours per day.
iii. her weekly income in rupees if she works 5 days a week. [Use £1 = Rs.133.2]
8. (a) Panna Kaji needs $6000 for his tour. How much money does he need if $ 1 = Rs. 105.15
and the bank takes the commission of 2%?
(b) Shaily is planning to visit Europe and she needs 3500 Euros. How much money does
she need if 1 Euro = Rs. 113 and the bank takes the commission of 2%?
(c) A man has to send £1500 to the UK for his sons study. How much money does he
need if the bank takes a commission of 1.5% and the exchange rate is £ 1 = Rs. 132.91?

Oasis School Mathematics-10 41

9. (a) A man converted Rs.7,34,500 into Euros for his business. After one week, the

Nepali currency is devaluated by 2%. If the exchange rate before the devaluation was
1 Euro = Rs. 113, find -
i. new exchange rate
ii. his profit or loss.
(b) A man converted Rs. 5,00,000 into Euro using the rate 1 Euro = Rs. 125. Immediately
after that Nepali currency is devaluated by 2% and he again converted Euro into
Nepali currency. Find
(i) new rate of exchange (ii) his profit or loss by the devaluation of Nepali currency.

10. (a) A laptop is bought in the Indian market at Rs. 15,000 I.C.

i. find its price in N.C. if 50% custom is added.

ii. find its selling price if 13% VAT is added while selling.

(b) A machine is bought in China at 2700 Chinese Yuan-

i. find its price in the Nepali market if 80% customs duty is added.

ii. find its selling price if it is sold at a profit of 20%.

iii. how much does a customer have to pay if 13% VAT is levied?

[Given 1 Chinese yuan = Rs. 15.60]

(c) A merchant bought 15 tolas of gold at 350 U.S. Dollars per tola. What should be its

cost in the Nepali market after paying 20% custom and adding 13% VAT.

[Given 1 U.S. Dollar = Rs. 108.18]

(d) Senmikha bought a photocopy machine from Japan at 2,50,000 Japanese Yen. It is

imported to Nepal after paying 30% transportation charge and 120% customs duty. If

he wants to make a profit of 80% on his total expenditure, find the selling price of the

machine in Nepali market including 13% VAT. Given that 10 Japanese Yen = Rs. 9.40.

11. (a) The aeroplane fare from Kathmandu to Bangkok is Rs. 25,000 and from Bangkok to
Kathmandu is 6,000 Thai Baht. Which one is cheaper?

(b) In the Nepali market, the cost of ghee is Rs. 800 per kg. In the Indian market, the cost
is Rs. 500 per kg. Find which market is cheaper one and by what percent?

12. (a) Santosh bought 15 Nepali handicrafts at the rate of Rs. 1,800 per piece. He paid 10%
export tax and sold them for 20 Euros per piece in Europe. Find his profit or loss.

(b) Lakpa bought 600 Thanka at the rate of Rs. 800 per piece. He paid 15% export tax and
sold them at £15 per piece in London, find how much profit he made. Also find the
profit percentage.

(c) Ram Bharosh bought 120 carved windows at the rate of Rs. 2,500 per piece. After
paying 10% export tax, at what rate should he sell it in Japan to make a profit of 50%.

13. (a) A man converted Rs. 9,45,000 into Euro for his Europe tour at the rate of 1 Euro = Rs.
135. Later on his tour was cancelled because of the effect of Covid-19. At the same time
Nepali currency is devaluated by 5%, find his profit or loss.

42 Oasis School Mathematics-10

(b) A man converted Rs. 5,00,000 to Euro for his Europe tour at the rate of 1 Euro = Rs. 130.
He spent 500 Euro on his tour and returned back to Nepal. Find much Nepali currency
is left with him?

(c) A businessman converted Rs. 8,80,000 into American dollar at the rate of 1 dollar = Rs.
110. Altogether he spend 5000 dollar. During that time Nepali currency is devaluated
by 2%, find how much Nepali currency is left with him.

Answers

1. (a) Rs. 16,227 (b) Rs. 33,227.50 (c) Rs. 48,025 (d) Rs. 14,855 (e) Rs. 16,960

2. (a) (i) 554.63 US Dollar (ii) 530.97 Euro (iii) Rs. 37,500 (iv) £451.43 (v) 3853.56 Chinese yuan

(vi) 19,933.55 Thai baht (b) (i) 26,910.65 Japanese yen (ii) 332.62 Singapore Dollar

(iii) 310.37 Canadian Dollar (iv) 844.02 UAE dirham (v) 235.92 Swiss france

3. (a) (i) 181.75 US. Dollar (ii) 4,29,849.3 Japanese Yen (iii) Rs. 22,221.56, (iv) 165.87 Euro

(b) (i) 1.23 U.S. Dollar (ii) 7.23 Chinese yuan (iii) 8749.46 Japanese yen, (iv) Rs. 17363.40

4. (a) Rs.4,800 (b) Rs. 10,400 (c) (i) 349.34 Euro, (ii) Rs. 6,83,220 (d) Rs. 80.05

5. (a) 408.41 (b) Rs. 9.75 6. (a) Rs. 115.50 (b) Rs. 120.36, Rs. 24072 (c) Rs. 142.80, Rs. 7140, 420.17 pound

7. (a) (i) Rs. 26,91.84 (ii) Rs. 24,226.76, (b) (i) Rs.725.40 (ii) Rs. 7,254, (iii) Rs. 217620 (c) (i) Rs.

5994 (ii) Rs. 41,958 (iii) Rs. 209790

8. (a) Rs. 6,43,518 (b) Rs. 4,03,410 (c) Rs. 2,02,355.48 9. (a) (i) 1 Euro = Rs. 115.26

(ii) Profit = Rs. 14,690, (b) (i) Rs. 127.50 (ii) Profit Rs. 10,000

10. (a) (i) Rs. 36,000 (ii) Rs. 40,680, (b) (i) Rs. 75,816, (ii) Rs. 90,979.20, (iii) Rs. 1,02,806.50

(c) Rs. 51,342.23 per tola (d) Rs. 11,98,975

11. (a) From Bangkok to Kathmandu (b) Same price

12. (a) Profit = Rs. 4200 (b) Profit = Rs. 6,44,190, 116.7% (c) 4464.28 yen per piece

13. (a) Profit = Rs. 47, 250, (b) Rs. 4500 (c) Rs. 3,36,600

Project Work

1. Collect the names of 10 people from your family or locality who are working
in foreign country and from the source of the family ask their monthly income.
Go through the exchange rate in the daily papers, convert their income into
Nepali currency and present that in your class.

2. See the price of gold, silver and oil in the international market (in U.S. Dollar)
and find out the rate of custom duty, VAT, etc. Convert their price into Nepali
currency, including all taxes. Present your report in class.

Oasis School Mathematics-10 43

Unit

3 Compound Interest

3.1 Warm-up Activities

Discuss the following in your class and draw a conclusion.
A man kept Rs. 5000 in a bank for a year. What is the simple interest at the rate of 10%

p.a.?
In this question,
What is the value of principal (P)?
What is the value of rate (R)?
If the time is 1 year, how to calculate simple interest (I)?
What is the relation among P, T, R and I?
How to calculate the amount?
Again, what does rate of interest mean?
If the rate of interest is 10% p.a., what does it mean?

Remember!
Interest of Rs. 100 in 1 year is the rate of interest.

If the interest of Rs. 100 in 1 year is Rs. 12, rate of interest is 12%. With the help of the
above information, find the rate of interest if,

• interest per rupee per year is 9 paisa.
• interest per rupee per month is 1 paisa.

3.2 Compound Interest

Let's compare two different examples
Suntali took a loan of Rs. 5,000 at the rate of 8% p.a. for 2 years. How much interest does

she have to pay?
Chameli took a loan of Rs. 5,000 at the rate of 5% p.a. for 2 years. After one year, the

interest of the first year is added to the principal. How much interest does she have to
pay in 2 years?
In the first example, the interest that Suntali has to pay is simple interest.
In the second example, since the interest of the first year is added to the principal,
Chameli has to pay the interest of the interest of first year also. So it is a compound
interest.
If the principal remains the same for the entire period, it is called the simple interest.

44 Oasis School Mathematics-10