PRACTICE MATH AFER SEE

CONTENTS

1. SET RELATION AND FUNCTION....*.... ...10

2. NUMBERSYSTEM. ***.. 18

3. TIME AND WORK. ****..25

4. PERCENTAGE... s***... 31

5. PROFITAND LOSS.... 37ee*****.

6. INTEREST AND POPULATION GROWTTHH....o ***.... 44

7. MENSURATION. .se.+*ee*e*e* *.... S9

8. ALGEBRA. .. ......63

9. SURD AND INDICES ..... ..71

10. QUADRATIC EQUATION. .76
1l. RATIO AND PROPORTION .82

12. SEQUENCE AND SERIES ***..90

13. TRIGONOMETRY...**.**. ..101

14. SLOPE AŅD STRAIGHT LINES 105
.I14
15. ANGLES AND TRIANGLES....
*****. 121
16. QUADRILATERAL AND PARALLELOGRAMS.. 130

17. CIRCLE AND ITS PROPERTIES... 138

18. PROBABILITY.... eeeeeeee 145

19. STATISTICS..

20. PASTQUESTIONS..

Chapter-1

SET RELATION AND FUNCTION

1. Set:

Any well-defined collection of distinct objects is called set.

Any object in a set are called its member or element.
E.g.: The collection of SAARC countries is set.

The collection of prime number is set.

2. Cardinal number of a set:

Totality of distinct elements in the set.

The cardinal number of set A is denoted by n(A)

3. Types of set:

a. Empty set [Null set]: A set having no elements is called
empty set. E.g. The set of boys in Kanya campus.

b. Singleton set: A set contain only one element is called
singleton set. E.g: The set of even number between 5 and

7.

C. Finite and infinite set: A set contain finite number of

elements is called finite set, otherwise infinite set. E.g.:
The set of prime numbers between 1 and 20 is Finite set

but A ={1, 2, ........ is an infinite set.

d. Equal sets: Two or more than two sets are said to be equal

if they have sameelement. E.g. If A = {1, 2, 3} and B=
{3,2, 1} then A and B are equal sets. In symbolically A =
B.

e. Equivalent sets: Two sets A and B are said to be

equivalent if they havesamecardinality. E.g. A = {a, b,c,

d} and B={ 1,2, 3, 4 } then A and B are equivalent sets.

f. Over lapping sets (Inter section sets): Two sets A and B

are said to be overlapping if they have at least one

commonelementE.g. A = {p, q, r}and B={r, s,t} are

overlapping sets.

Disjoint sets: Two sets are said to be disjoint If they have

nocommonelemenEt .g. : A{4, 5, 6} andB ={7, 8,9}

are disjoint sets.

1

h. Subset: A set A is said to be a subset of set B if every
element of set A is also an element of set B. It is denoted

by Ac B.

i. Proper and improper subset: A set A is said to be proper

subset of B if every element of A is in B and at least one
element of B is not in A. It is denoted by AcB. Otherwise
it is called improper subset.

Power set: The set of all possible subsets of a given set A
is called the power set of A. It is denoted by P (A).

k. Universal set: Largest set under consideration as subsets

is called the universal set. It is denoted by U.

Note: Every equal sets are equivalent sets but converse may not
be hold.

4. Operation on sets:

a. Union of sets: The union of two sets A and B is the set of
all elements which belongs either to A or to B, or both A
and B. It is denoted by A u B. Symbolically, it is defined

as ;

AUB= {x:xE A or xe B}

b. Intersection of sets: If A and B are any two sets then the

intersection of A and B is the set, whose elements are

common to both A and B. It is denoted by AnB.

Symbolically it is defined A n B= (x: xe A and xe B}

C. Difference of sets: If A and B are any two sets, then
difference of set A to B is the set of all the members of set A

which are not in set B. It isdenoted by A - B. Symbolically it

isdefinedas: An B= {x:xe Aandx B}

Similarly: A-B= {x: xe B, xe A} of set A is

Note:A -BB-A

d. Complement of a set : The complement

denoted by à or A°, symbolically it is defined as:

Ā = {x :xe Uand xe A}

5. Symmetric difference:

Symmetric difference of any two sets A and B is set of all
members of A and B, Which are not common elements to A

2

and B. It is denoted by A AB (A delta B). Symbolicaly it is

definedas A A B=(A-B)(B - A)

Or, A A B= (A UB)-(AB)
6. Properties of set operations:

a. Idempotent laws:

AUA= A, AnA =A

b. Identity laws:

Au=A, An=¢,AUU=U,AnU=A

C. Commutative laws :

AUB=BUA andAo B=BoA

d. Associativelaws:
(A UB) UC=AU(BUC)

(AnB)nC=An (AnB)

e. Distributive laws:

AU(BAC)= (AUB) n(AU)

AnBUC) = (AnB) U (AnC)

f. Complement laws:

Ā =A,Ū -, AUĀ=U

De-Morgan'slaws:

AUB=ÃUB and ÁnB=ÃOB

7. Important results of set.

a. n(A UB) = n(A) + n(B) - n(AnB)[For overlappingset)

b n(A U B) = n(A) + n(B) [for disjoint set]
C n(A - B) = n(A)-n(A oB)

d. n(A UB)=n(U)-n(AUB)

e n(A U BUC)=n (A) + n(B) + n(C) - n(AnB) - n(B

C)-n(Anc) + n(An BoC).

8. Orderd pair:

A pair of two elements in which if their order is important then

it is known as ordered pair. It is denoted by (a, b)

Note : (a, b) (6, a)

3

9 Cartesian product:

Consider two sets A and B. The Cartesian product of A and B is
denoted by A x B and is defined as the set of all ordered pairs
(a, b) in which a is the element of A and b is the element of B.

Symbolically, A x B ={(a, b); ae A and b e B}

10. Relation:

A relation from A to B is subset of Cartesian product A x B. It

is denoted by a R b.

Note
a Domain:

The domain of the relation is the set of all the first element of
the ordered pairs of the relation.

b. Range:

The range of the relation is the set of all the second element of
the ordered pairs of the relation.

b. Co-domnain :
The whole second set is called co-domain of relation.

11. Function:

A function from a set A to B is a particular case of relation in

which each element of a A corresponds to unique element of B.

12. Composite function:

Let f: A → B and g: B → C. Then composites function from A
to B is denoted by (gof) (3) = g(f(x).

Note: If n(A) = m, then

No. of subsets = 2m

No. of empty subset = 1

No. of non empty subset = 2m- 1

No.ofpropesr ubsets 2"-1

No. of non-emptysubsets= 2m-2

No. of improper subset = 1 (itself)

Objective Questions

1. If (An A)=¢,then A-A is

a {0} b. {4}

c. A d. {A}

2. An empty set is

a set having no subset
b a set having no super set
C. a set having no element
d. a set having only one element zero

3. A universal sets is

the superset of every set under consideration
b. the subset of every set under consideration
C. the set of all real number
d. the set of complex numbers

4. IfA= {1,3, 5, 7} and B= (2,4, 5, 6, 7}, then A- (ANB)=

a. {1, 3, 5, 7} b. {2, 4, 5, 6, 7}

c. {1,3} d. {1,3,2,4,6}

5. IfA= {1, 2, 3, 4} and B= {3,4,5, 6} then AUB is

a. {1, 2, 3, 4, 5, 6} b. {3,4}

c. {1,2} d. {5,6}

6. IfA ={1, 2, 3, 4} and B= (3,4,5, 6} then AAB

a. {1,2, 3, 4, 5, 6} b. {3,4}

c. {1, 2} d. {1,2, 5, 6}

7. IfA={1, 2, 3, 4} and B=3,4, 5, 6] then A -B is

a. {1, 2, 3, 4, 5, 6] b. {3,4}

c. {1, 2} d. {5, 6}
8. Which is true?

a. AnB={x:x* A or x¢ B}

b. AnB ={x:x¢ A or xe B}

C. AnB= (x:xE A or xe B}

d. An B ={x:xE A and xe B}

5

9. {f, r, e, e} is same as b. {f, r, r, e, e}
a. {f, r, e} d. all of these

c. {f, f,r, e, e}

10. Sets A and B have n(A) and n(B) elements each. What can

be the maximum number of elements in AUB?

a. n(A)-n(B) b. n(A) + n(B)

c. n(AnB) d. n(A) + n(B) – n(ArB)

11. A and B have 3 and 6 elements each. What can be the

minimum number ofelementsin AB?

a.3 b. 6

C. 9 d. 18

12. A and B two subsets of a universal set 'U' in which n(U) =

80, n(A) = 50, n(B) = 30 and n(AnB) =10. Find the value of

n(AUB). b. 50

a 80 d. 10

C. 70

13. IfU= (x:x is a positive integers less than 16}, A={5, 10, 15}

and B={2, 4, 6, 10}, find AnB

a. {1, 3, 7, 9, 11, 12, 14}
b. {1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15}
c. (1,7, 9, 11, 12, 13, 14}
d. {1, 3, 7,9, 10, 11, 12, 13, 14}

14. IfU = (4, b, c, d, e, f, g} and A={e, e, g} find (A)'

a. {a, b, d, e, f} b. {a, b, c, d, e, fg)
C. {C, e, g}
d {a, b, d, f, g}

15. Which is true? (for two sets and A)

a. e A b. cA

c. {0}e A d. acA

16. Which is true? b. 0

a. ={o} d. ={}

C. =0

6

17. If AnB=then,

a. AcB b. BeĀ
C. AçB d. BcA

18. IfU={ 1,2, ., 10}A =(Primenumber<10},B={odd

number less than 10} then, A -B is

a. {2} b. {5, 7}

c. {1,3} d. None

19. IfP= (a, b, e, d}, Q ={e, b, f and R=h, i, e, b} then which

of the following statement is wrong.

a. (PoR)cQ b. (Po Q)CR

c. (Qn R) CP d. both a and b

20. The total number of subset of given set A = {5, 6,7, 8} is

a. 8 31El ishtb. 14 8S

C. 16 d. 20

21. II U={x: 2<x+1<11}, A = {x :x is anevennumber}, B

={x:x is a prime number}. Find the set of elements which

are neither even nor prime?

a. {1, 7, 9} b. {9}

C. {1, 8, 9} d. (2, 3, 5, 7}

22. The set (A -B)U (B- A) U (AnB) is equal to the set

a. AUB b. AUB

C. AOB d. ĀnB

23. Which of the following is a single ton set?

a. b. 0

c. {} d. {0}

24. If f()=3x-9,thena)a--1bb

a. -3 b. -1

C. 0 2 ik bnd. 3

7

125. If f()sinxthen

a. (x)-0 b. f(-x)=-f(x)

c. f(x) =-f(x) d. f-x)=f

26. If AcB thenwhichoneistrue?

a. BcA b. BɔĀ

C. AUB=A b. AnB=B

27. IfAnB=¢, then

a. Boà =B b. BoA =BUA

C. BcA d. AcB

28. If number of proper subset of set A is 31 then n(A) =

a. 4 b. 5

C. 6 d. 7

29. The number of non-empty sub sets of set B is 63, then n(B)

a. 5 b. 6
C. 7 d. 8

30. Which of the following is a null set ?

a. {x:x=0)

b. (x:x*-2=0, xisrational}
c. (x:x-4= 0}

d The set of circles passing through three collinear points

31. IIAXB= {(1, 2), (2, 5),(2, 3)} then A is

a. {1,3} b. {(3, 5}

c. {1, 2} d. {2,3}

32. Set A and B have 3 and 6 elements respectively. What can

be the maximum number of elements in AUB?

a.3 b 6

C. 9 d. 18

33. The set S = {x:x* +6=0 and x is real) is

a. Singleton set b A pair set

C. A null set d. symmetric set

8

34. If f(x) = x +1 and g(x)= 2x' +1 theng.f (x) is

a. 2x' +1 b. 2x +2

C. 2x + 4x+3 d. x'+1

35. If A is the set of integers and B is the set of natural

numbers then

a. A-B= b. AUB=B

c. B-A= d. AnB=A

36. Find the value of k ifx -2 is a factor of 2kx* 3x +2

a. 2 b. 1 ese

C. d. -1 te

37. The domain of f(x) (g-1)j is:

a. R-{0} b. R-{1}

c. R d. R-{2}uh

38. Iff: A B defined by f(x) = 2x+3 and A={2,4,5,6, then

Range set is:

a. {7,11,13, 15} b. {7,11,13, 14}

C. {7,8,9,10} d. {8,9,10,11}

Answers:

1. C |2 a 4. c 5. a 6. dI7. :8. d9. d b

11. b 12. d 13. b14. c 15. b16. d 17. a 18. a 19. d 20. c
21. b 22, a23. d |24.d 25. b |26. a27. a|28. b 29.b B0. d
31. c 32. c33. c 34. c 35. c36. d 37 b 38 a

Chapter

NUMBER SYSTEM

1. Classification of Numbers

a. Nature number: The set is counting numbers is called
natural numbers. It is denoted by N, then N={1, 2, 3, 4, 5,

b. Whole number: The set of natural numbers including
zero (0) is called whole numbers. The set of whole

numbersisdenotedby W, then W= {0, 1,2,...

c. Integers: The set of natural numbers together with their
negative and including zero is called integers. The set of

integersisdenotedby Z, then Z = {..,-2, -1,0, 1,2, .,

d Prime number: A number is said to be prime if it is

divisible by anditself only.ish

te. Composite number: A number is said to be composite of
it is divisible by other than 1 and itself.
Note: 1 is neither prime nor composite.

f. Rational numbers: The set of rational numbers denoted
by Q. is the set of all numbers of the form where P and

q are integers, and q # 0.

Insymbol,Q= ip & qareintegersandq # 0}

g. Irrational numbers: The set of numbers which can not be

expressed in the form where p and q are integers, q # o.

It is denoted by Ir.
h. Real numbers: The set of numbers which contains both

rational and irrational numbers. It is denoted by R.

classification of real numbers as follow.

10

Real Numbers

Rational Numbers Irrational Numbers

Integers Fractionsp ih

- Positive integers (Natural Numbers)

Zero

-Negative integers

The family members of the real numbers have the following set

relation: NcZcQcR 10

Inequality

a, b and c are three real numbers 0*10

a. If a >bthena + c>btc

b. If a<bthena -c <b-c

C. Ifa> b then ac > bc, when c> 0

d. If a > bthen ac < bc,whenc <0

e. If a> b then>when c> 0

f. Ifa> b then< when c<0
C

g. Ifa > bthen a <b. achtn egoue

Interval 93

1. Open-Interval

(a,b)={x: a<x<b}al

a tbb

2. Closed-Interval
[a, b] = {x: asxs b}

1

3. Left open interval

(a, b] = {x:a<xsb}

b

4. Right open interval

[a,b) = (x: asx<b}

a viii

Absolute value

b Let x denote any real number. The absolute value (or modulus

or numerical value) of x. Written as (x|, is non-negative real number

defined by:

x forx 0

-x forx<0

E.g. -3|=3) =3

|3|=3

Note:

1. VaxVb =yab is a, b> 0 or either one is zero.

2. Vaxy =-Vab ifa,b<0

3. =-1 or, i =-1 (wherei istheimaginaryunit)

Note:

a. Rational numbers can be expressed as terminating or

recurring decimals.

b. Irrational numbers are neither terminating and non

recuring.

C The set Z & R closed under the operation of addițion
subtraction and multiplication.

d. Additive and multiplicative identity of rational number are

0 &l.

e. Additive & multiplicative inverse of any rational number
'a" are (-a) & 1/a.

12

2. HCF and LCM

a. HCF (Highest Common Factor): The greater number
which divides all the given numbers without remainder is
called HCF.

b. LCM (Lowest Common Multiple): The least number
which is divisible each given numbers exactly.

C Relation between HCF and LCM.

[LCM x HCF = Product two given numbers]

Objective Questions

1. Whichis a irrational number?

a. 3.725 b. 2.451253....

C. 1.234234 d. 5.242424

2. Which one is odd prime number?

a. b. 3

C. 9 d

3. Multiplicative inverse of (5a-7) is the a is equal to

a. 2 b. 14

t44c. d. Ss4pe 193

4. Which one is even prime number?

a. 2 b4

C. 6 d. 8i
5. Find H.C.F. of numbers 144, 96 and 72.

a. 72 b. 36

C. 24 d. 12

6. Find L.C.M. of 21 and 51.

a. 357 b. 375 9

c. 573

7. H.C.F of 250, 280 and 320 is

a. 5 b. 10

C. 20 d. 25

13

8 Find L.C.M of 24, 20 and 15.

a. 30 b. 60

C. 120 nd. 240

9 Find L.C.M of 40, 50, 60 and 100.

a. 100 b 300

C. 600 d 900

10. What is the least number which when divide by 100, 120

and 15Q leave a remainder 2 in each case.

a. 902 b 602
c. S02
d 702

11. Find the greatest number which can divide 324 and 432
without a remainder.

a. 108 b. 150
d. 250
C. 216

12. If the H.C.F. of 105 and 150 is 15, find their L.C.M.

a. 1250 b. 1005

C. 1500 d 1050

13. What is the cube root of 4096?

a. 12 b. 14
d. 18
C. 16

14. What should be subtracted from 2210 to get the reminder a
perfect square?

a. b. 2

C. 3 d. 4

15. 60 Bananas and 140 apples are to be distributed equally

among a number of girls. Find the greatest number of girls
receiving the fruits in this ways.

a. 12 b. 15

C. 20 d. 35

16. Two bells rings at the intervals of 20 and 30 minutes

respectively. If they ring at 12 pm .When will they rang
together again?

a. Ipm b. 2pm

C. 2:30pm d. 1:30Pm

14

17. Thesolution of the inequality 2x + 1> x +3 will be

a. x>2 b. x<2

C. X=2 d zero

18. A number multiplied by two third of itself makes the

product10584thennumberis ede 5

a. 123 b. 124

C. 125 d. 126

19. x is anevenpositiveintegerthen otherconsecutiveeven

integer is

a. (x+ 1) b. (x+2)

C. 2x d. x

20. Suppose x is divisible by 8 but not by 3.Then which of the
following can't be an integer?

X X

a.

X

C. d. 8

21. If0 <x<1, which ofthefollowingsetsare in theincreasing

order?

a Vx, x,x b. x,x, V
d. x,yx,x
c. x,x*,Vx

22. If3- x 3'= 3", what is thearithmeticmeanof x and y?

a. 50 b. 100

C. 25 d. 200

23. If x -y ispositivethenwhich of the followingstatementis

true? s

a. 0>x>y b. x>0>y

C. y>x>0 d. botha and b

24. Ifx is an integer and 3x + 11 is even, which of the following

must beeven? iuaseh LE-)edt ae

a. X b. x+ 1

C. x? d. 2x+ 1

25. What is the smallest positive number, other than 2, when it

is divided by 3, 4 and 5 will leave a remainder of 2?

a 62 b. 42

C. 22 d. 182

15

26. The product of six integers is negative and then at most how

many of the six integers could be negative?

a. 3 b. 4

27. If x <y <-1, whichis ofthefollowingexpressionhasthe

greatest possible value?

b
X
ala y
C. d.

28. Which of the following cannot be expressed as the sum of
two or more consecutive positive integers:

a. 17 b. 22

c. 24 d. 32

29. If n is divided by 9, the remainder is 5, what is the

remainder if 3n is divided by9.

a4 b5

c6 d None

30. Ifa x b xc=72, where a, b, c are integers and a> b>c>1,

what is the greatest possible value of a?

a. 12 b 18

c 24 d. 36

31. Three times the first of three consecutive odd integers is 3
more than twice the last. The first integer is

a. b. 9

C. 11 d 13

32. If0<p<q<1, which of thefollowingistrue?

a. 9-p is negative b is positive

C 1ispositive d. none of them

33. The value of k such that (2k-1) is additive inverse of -7/

a. 3 b. 4

C. 5 d. 6

34. Thevalueof N2 x\3is

a. b. V6

6C. d 2

16

35. The cost of a pen is Rs. 15. Find the maximum number of
pens that can be purchased for Rs 200.

a. b. 12

C 13 d. 14

36. The half plane y x+1 contains the point

a. (3, 3) b. (1, 3)

C. (0, 0) d. (2, 2)

Answers: c 4. a 5. c6. a 7. b 8. c 9. c 10. b
c 14. a 15.
1. b 2. b 3. a l6. a 17. a 18. d 19. b 20. c
|11. a 12 d 13. d 24. b 25.
d 26. c 27. d 28. a 29. c 30. a
|21. b 22. a 23. b 34. b 35.
c 36. b
31. c 32. b 33.

17

i Cxhapte

TIME AND WORK

1) Variations:

Direct Variation: The relation between two quantities

such as one increase then another also increases; same as
one decreases then another also decreases this relation is

called direct variation.

b. Indirect variation: In the relation between two quantities

such that one increases then another decreases and vice
versa is called indirect variation.

Note:

a) More speed of vehicle less time taken so it is indirect relation.

b) 100 kg. = l quintal l inch = 2.54 cm

1000 kg. =1 Tone 1 feet = 12 inch

1 kg. = 1000gm I meter =39.37 inch

1 kg. =2.2046 pounds I meter =3.2808 feet

Igm = 1000 mg I mile = 1.6 km

ObjectiveQuestion

1, Arun & Barun finish a piece of work in 10 days. Barun
alone takes 15 days to finish it. Arun alone can finish it in

a. 15 days b. 12 days

C. 25 days d. 30 days
I2. If 25 liters of petrol costsRs 1400, what will be the cost of 9
liters?

a. Rs 504 b. Rs 405

C. Rs 540 d. Rs 450

3. If the cost of 4 pens is Rs 48, how many more pens can be

bought for Rs 120?

a. 8 b. 10 985 y
C. 12 d. 15 gi t

1207 4120 10

18

4. If 100 pens cost Rs 984, how many pens can be bought for
Rs 246?

a. 22 Dus d. 33 I Ey

C. 30

5. If9 men can do a piece of work in 10 days, how long will 15
men take to do it?

a. 4 days b. 5days usiil s139 t

C. 6 days a. 7; days

b

6. If 8 pieces of goods costs Rs 192, what will be the co of 1144

pieces of same goods?

a. Rs. 633 b. Rs 363

C. Rs 360 d. Rs 336

7. 5 men take 6 days to complete a piece, of work. How many

longdoes it take to complete the sare work by 15 men?

a. 4 days b. 3 day

C. 2 days d day

8. If a boy walks 16 km in Z days, in how many days will he

walk 256 km?

a. 24 days b 30 days

c. 32 days d. 1 days

9. If 32 mer can finish a work in 96 days, how many inen can

finishame work in 64days? 2i4

a. 40 d. 60b.u48 ot r
C. 56

Ypo. How many miles does a car travel if it average a rate: of 35

miles per hour for 3 hour and 24 minute?"? 212
30ma. 119
b. 109

C. 129 d. 113

11. If 15 kg of rice costs Rs 405, what is the cost of 21 kg of

a. Rs 675 b. Rs 760
C. Rs 720 d. Rs 567

19

12. The bus fare of 30 passengers is Rs 900. What is the rent of
18passengers if the rate of fare is increased by Rs 10?

a. Rs 660 b. Rs 700

C. Rs 720 d. Rs S67 ohH3 98en

13. How long would it take a car travelling at 30 miles per hour
to cover a distance of4 kilometer?

a. I minute b. Sminutes

c. 25 second d. 1 second

14. Ifl quintal of rice costsRs 2100, what is the cost of 45 kg of
rice?

a. Rs 549 b. Rs 495

C. Rs 750 d. Rs 945

15. Porter charge to carry a bag of 50 kg of rice to a distance of

4 km is Rs 200. What is the charge to carry the bag of 80 kg

of raice to a distance of l0 km?

a. Rs 800 s b. Rs 500 V ndn1
C. Rs 7S0
E d. Rs 1000

Ir16. of rice is 56 kg, what will be the weight of of it?

a. 80kg b. 70 kg
d. 50 kg
C. 60 kg

17. Hari can do of a piece of work in 8 days. How many days

will he take to do the whole work?

a. 15 days b. 12 days

C. 6 days d. 4 days

18. If 18 men can complete a piece of work in 45 days, how

many more men should be employed to complete the work
in 15 days earlier?

a. 27 b. 36

C. 5-4 d. 9 hio 9o11 to gd

19. How many days do 7 men take to do a work if the work is

finistied by 10 men in 5 days?

a. 7; days b. ;days

C. 7 days d. 8 days

20

20. How many laborers in 21 days will do the work done by 112
labors in 27 days?

a. 144 b. 108

c. 88 d. 160

21. If 5 pumps can fill 200 liter of water in 30 minute, how

many pumps of the same size are needed to fill 960 liter of
water in 20 minutes?

a. 40 pumps b. 30 pumps

a c. 36 pumps d. 16 pumps

22. Chante paid Rs 510 as income tax when it was S paisa per

rupee. What was his income?

a. Rs 5,100 b Rs 5,010

C. Rs 12000 d. Rs 10,200

23. If the price of 3 kg of tea is equal to the price of 10 kg sugar,

what is amount of tea can be exchanged with 25 kg of

sugar?

a. 12 kg b. 8 kg

c. 9 kg d. 7z kg

24. The cost of 12 books is same as the cost of 20 pens. If the
cost of 8 pens is Rs 240, find the cost of 8 books

Rs 200 b. Rs 400

C. Rs 600 d Rs 800

25. If a motorbike runs at a speed of 96km per hour, how far
will it go in 10 min?

c.a. 4.8 Km b. 16 km
km d. 12 km

26. 15 men can do a work in 4 days. In how many days can 10

men the same work?

a. 3 days b. 6 days

9 days d. 10 days

27. Anju bought 40 bags of Rs 35 each. If the price rises to Rs

40 how many bags could then be bought?

a. 40 bags b. 30 bags

C. 25 bags d. 35 bags

21

28. If16 students consume 192 kg of rice in 8 days, what quality

will be 4 students consume in 10 days?

a 40kg b. 50 Kg

C. 60 kg d. 75 kg

29. 27 laborers can dig a field in 15 days. How many laborers

can dig the same field in 9 days?

a 45 b. 48

C. 52 d 60

30. Arun can do a piece of work in 6 days and Bina can do it in

12 days. In how many days would they finished the work if
they work together?

a. 2 days b. 4 days

C. 6 days d. 12 days

31. Find the amount of medicine required to administer for

seven day, 4 times each day at. the rate of 500 mg each time.

a. 14 gm b. 15gm

C. 16gm d 12 gm

32. Two pipes can fill an empty tank in 40 minutes and in 1

hour's respectively. If they both the pipes are opened at

once, how long would they take to fill the tank?

a. 18 min b 30 min

C. 12 min d. 24 min

33. Ir"of rodisequalto2mW. hatis of it?

a. 3.75 m b. 3.5 m

C. 3m d. 2.5 n

34. 20 men can finish a piece of work: in 30 days, how many

additional men required for leave the work, so that it may
be finished in 20 days. Eb. 10

5

C. 7 d. 21

35. Narayan can do a piece of work in 2 days and Punya in 3

days. How long will they take to do the work together?

a. 2 days b. 3 days

c. 2days d. i; days

22

36. of incomeof Vinod is Rs1600,fin of hisincome.

a. Rs 1200 b. Rs 1000
d. Rs 900
C. Rs 800

37. In question paper of an exam, there are 15 questions, eachı

question of equal marks the full mark is 1.00. If Santosh

scored 60 marks. How many questions dlid he attempt
correctly at least?

a. 5 b. 6 i c

C. 89 d.

38. Food is sufficient for 1200 soldier for 60 days. How long will
the food last for 1000 soldier?

a. 60 days b. 70 days

C. 72 days d. 80 days

39. Manju can do 4/5 of work in 20 days. But Manju and Bindu

can finished the remaining work in 3 days. How many days
will Bindu take to do the whole work alonė?

a. 35 days b. 375 days

C. 40 days d. 45 days

40. A garrison of 960 men has food enough to last for 65 days.

How many men should be sent away so that the provision
may last for 120 days?

a. 440 b. 520
C. 220
d. 630
41. A poll is filled to
of itscapacity1, of the water get

evaporated. if the capacity of the pool is 24,000 gallons
when it is full. How many gallons of water is to be added to
fill the pool?

a 8000 b. 6000

C. 12000 d. 18000

42. A bus moving with a velocity of 60km/hr covers 420km in 7

hours. How long does it take to cover 960 km with a velocity
of 40 km/hr?

a. 24 hrs b. 16 hrs

C. 12 hrs d. 6 hrs

23

43. Ir of the 350 students are girls at NAME, and zof the

girls play on a team, how many girls do not play on a team.

a. 150 b. 25
d. 175
C. 125

44. One Monday, a score owner received a shipment of book.
ileos
On Tuesday she sold half of them on Wednesday after two

more sold, she had exactly of the book left. How many

books were in the shipment.

a. 10 b. 20 nstlue 2i boo4

C.30 wi e d. 40

45. If 10 cow eat as much as 6 oxen, how many oxen will eat as

much as 150 cows?

a. 10 b. 6

BkSi c. 9 d. 42

46. At a speed of 48 miles per hour, how many minutes will be
required to drive 32 miles?

a. 40 b. 45

c. 50 60

47. Rs. 1360 have been divided among A, B, C such that A gets

21

7of what B gets and B gets of what C gets. Then B's

share is

a. Rs. 120 b. Rs. 160

C. Rs. 240 d. Rs. 320

48. Two ship leave from the same port at 11:30 A.M If one

sails due east at 20 miles per hour and other due south at 15

miles per hour, how many miles far the ship at 2:30 P. M.?

a. 75 b. 25
C. 50
d. 80

Answers:
4.2. a 3.
b5. c 6. d 7. b 0.
1. |12. c13. b14. d 15, a 16. c17.
b
21. d 22. d 23. d |24. b25. b 26. b |27, d 28. c 29. a30. b
31. 32. d 33. c 34. 35. d36. 1 37. d 38. c 39. b 40. A
41. a 42. a 43. b 44. b 45. c 46. a 47. 7 48. a

24

Chapter- 4

PERCENTAGE

1. Percentage:

The numerator value in a fractional number which has 100 in

denominatoirscallepdercentage. lpor

Thus,wehave 12005 =25 %,1X0o x%.

2, We use the symbol % to denote percentage.

3. Howtoconveprtercentageintofraction? tt oT

To convert percentage into fraction we omit the sign % and

divide the number 100 as, as1ani

XX%=00

4. How to convert fraçtion into percentage?

To convert fraction into percentage, we simply multiply the
fraction with 100 and use the symbol of percentage (%) as

by x 100 % p, q are integers, q #0
4

ForExample:Convert n intopercentage

40 x100%=5%

5, How to find the x% of y?

x%ofy =100 2

Note: To find the x% of y we use x/100 in the place of " x %"
and we use the sign of multiplication 'x' instead of " of".
6. To increase a number by x % we should multiply the given

mumbewr ith00 +x

100

Ex4mple:200isincreasedby40 %a18z 00 to ts

25

100 + 40
100 200

= 140 x 2=280

7. To decrease a number by x% we should multiply the given

number with10100-0 x

Example: 125isdecreasedby 20%.

100-–20 125
100

=40 x 5=100 t wki
8. To find increase % anddecrease%

Increase %= actualincrease
orginal

Decrease %: actuadlecreasex 100%

orginal

Objective Questions

1. The percentof is

a. 7% b. 20 % X loot
C. 27% d. 35%
test

2. % ofRs333 is... b. 66 103 of 33

a. 33

C. 111 4335d. 11

3. 75% of 1200 m is ....

a. 900 mm b. 900 cm

c. 9000 m d. 900 m

4 solo

What is the difference between and 75 %

a. 25% b. 50%
C. 75% d. 100%

5. Out of 200 examinees appearing in the S.L.C of 2050, if 50
examinees passed, find the fail percentage.

a. 2.5% b. 97.59% loot

C. 3% d. 75%

S1

6. 75% of student in Mangal Higher Secondaryare Newari. If

total number of students is 2000 .Find the number of non-
Newari students.

a. 250 Fox3 b. 375 woo
d. 150
C. S00

7. Out of 600 student, 200 were girls, what is the percentage of

boys?

a 40% b bAfeb.20%

C. 66% d. 60%

8. What percent is 120 of 90?

a 133% b. 100%

6%C. d. 33%

9. What percent of1 kg is 50 gm ? X t 8 Y of7Xa s 70 200

a 2. 5% b. 5%

C. 7.5 % d. 50%

10. When the price is increased by 8 % then value of

motoreycle will be 70,200. What is the value?S S

a. Rs. 60,000 b. Rs. 62,5000

C Rs 65000 d. Rs. 79,200

11. Find the sum of 15 % of Rs. 200 and 20 % of Rs. 150

a. Rs 60 I b. Rs. 30 I

C. Rs. 20 9 d. Rs. 40

12. What is the number whose 10 % is 12?

a. 100 b. 120

C. 105 d. 140 10 t w t ofBoy

13. What is 10 % of 20 % of 30 %? co t X

Fox38C. 0.6%
a 60)% b. 6% É Fox 3

d. 0.06 %

14. What is the number if 20 % of a number is 16?

a. 10 b. 20

C.. 40 d. 80

t

27

15. What is the amount whose 20 % is Rs. 60?

a. Rs. 100 b. Rs. 200 1k kn o2

c. Rs. 300 o00 a Rs. 6001ieu iat

16. If John saves Rs. 2000 after spending 60% . Find his
income.

a. Rs.12,500 b. Rs. 10,000 o

c. Rs. 7500 s8 h d. Rs.5000

17. What percent of vowel letters in the word "Geometry "?

a. 37.5 % b. 25% EX loot

C. 17.5 % d. 50%

18. The cost of 75 bananas is Rs. 50. If the cost is increased by
20 %. What will be cost of 120 bananas?

a. Rs. 96 b. Rs. 50

C. Rs.75 s d. Rs. 70

19. Whatismeantbypercentage? Ro tnsts sf

a. A part of 10 b. Apartof100

C. A part of 1000 0 d. A part of 100

20. If the number n isincreased by x %, then the number will be

100 100
a. 100+ x s
b. 100x Xn

C.1010+00X n t d. 100 +xn

100

21. If thenumberm isdecreasedbyy % then it will be

100%m 8 b. 1J0000+x mm a sd

a. 100 -y

100-my. Ed 100- m

100 100

22. Whatpercentageofonetoneis300 kee dl xshn d

a. 10% b. 20 %

C. 30% d. 60 % .

23. In the mixture of 20 L mlk and 30 L water, what are the
percentages of milk and water in the mixture?

a. 2/5 % & 3/5 % b. 2% & 3%

C. 20% & 30 % d. 40 % & 60 %

28

24. What percent of itself must be added from 60 to get 75?

a. 25% b 30%

C. 40 % d. 35%t

25. Ram get 60 % of total valid votes and beats his only one
opponent by 3000 votes. Find the number of the total valid
votes.

198 a. 9000 b. 12000

C. 15000 d. 18000

26. After paying an income tax of 5%, a man has Rs. 7600 left.
What is his income?

a. Rs. 800 b. Rs. 8000

C. Rs: 4000 d. Rs. 16000

27. The price of an imported car is 8,25,000 which includes a

VAT of 10% of the original cost. Find the price of the car
before VAT.

a. 8,25,000 b. 7,50,000

C. 75,000 d. 8,00000

28. When the rate of income tax is increased from 10% to 15%
have to pay Rs. 835 more, find income.

a. 16705 b. 16600

C. 16700 d. 18500

29. My salary was first increased by 10% and then decreased

by 10%. What is the total percentage changes in my salary?

a. 2.2% b. 1.5%

C. 1% d. 3%

30. A single discount equlvalent to the successtve discount 10%
and 5% will be

a. 14.5% b. 10%

C. 3.5% d. 8%

31. A Man's annual income is Rs 60000. The first 20000 is tax

free and he has to pay 5% on the next 20000 and 10% on

the remalnder. How much does he pay as Income tax per
year?

&. Rs. 2500 b. Rs. 2800

C. Rs. 3000 d. Rs. 3200

29

32. If the numbers 8 and 12 are increased by 25% and 33

respectively. What will be the average increment?

a 30% b. 15%

C 10% dme a asd. 20%

33. On a text consisting of 80 questions Ram answered 75% of

the first 60 questions correctly. What percent of the other

20 questions did she need to answered correctly for her

grade on the entire exam to be 80%

a. 85% b. 87.5% iud h

c. 90% d 95%

34. If 'a' is a positive number, 400% of a is what percent of

400a?

a. 0.01 b.0.1d on

C. 1 d. 10

Answers:

a 9. b 10. b

IL. 1 12. b 13. c14. d 15. e 16. d 17. a 18 a 19. b 20.
21. d 22. c 23. d 24. a 25. c 26. b 27. b 23. c29. c 30.

31. c32. a33. d34. c

s

30

Chapter

PROFIT AND LOSS

1) Selling price (S.P): price for which an article is sold.
2) Cost price (C. P): price for which an article is bought.

3) Profit: When selling price is greater than cost price then there is

profit. It is also known asgain.[i.e. S.P. >C.P.]tos
4) Loss: When cost price is more than selling price then thẹre is

loss. [i.e., C.P> S.P]

5) Marked price [M.P.J: The price written on the chit attached to
the article which kept in shops for sale is called the marked
price. It is also known ascatalogue price or list price.

6) Discount: It is an allowance of deduction of allows a
concession on the marked price,

T) Net price (Selling price): The price of an article after deduction
discount.

Note: I. Profit % and loss % always calculated on C.P.

II. Discount is always calculated on marked price.

Important Formulae

a) Actual profit (gain) = S.P. -C.P.

b) Actualloss =C.P.-S.P.

c) Profipt ercentage=-actuCalp.Pro. fit 100%
Loss percentage = actuCa.lPl.ossx 100%
3Ber

d)

e) When C.P. & profit % are given: S.P. = 100 +profit% X

100

C.P.

When C.P. and Loss % are given: S.P. =100–loss%

100

C.P.

Net price (Sellingprice ) = M.P., - discount

31

h) Discount- M.P. -S.P

i) Discount %= actual discount x100%
MP

1) If two successive discounts are d, % and dz % then:

S.P=(1g)(-100)f M.P.

Objective questions:

1. When an article is sold for a price higher than the cost price
there becomes.

a. Loss b. C.P.

C. Profit d. S.P.

2. Hari sells a radio for Rs. 550. If he makes a profit of 10%

on cost price, find the cost price. SP CP Profit

a Rs. 515 b. Rs.495 550 Cpt lot of CP

c. Rs. S00 d. Rs.50s I 1107 of CP

3. Barsha buys a bag for Rs. 650anatdasepllsrofit of 4%. Find the
selling price of that bag.
b Rs. 690 GSO TIX GSQ
a Rs. 676 d. Rs. 654 s 676

C. Rs.624

4. Find the profit percentage if an article costing Rs.500 is sold
for Rs.S60

a. 12% b. 30%

c. 70% d. 35%

5. Deepak bought a bag for Rs.320 and sold it at 15% profit,

find it's selling price.

a. Rs.480 b. Rs 368

C. Rs.335 d. Rs.350

6. 3%of 1000is X 1000

a. 25 b. 35 tho
C. 45 d. 3.5
z
35

7. Shushila sold a radio for Rs.126 at a loss of 10%. What is
the cost price of that radio?
SP s CP LOSS
a. Rs. 112 b. Rs. 140 126 s CP lot of CP
Rs. 160
C. Rs. 156 d. 126 got Of CP

32

8. Find out the cost price whose 18% profit is Rs.81.05

a. Rs. S40 b. Rs. 504 18 t of CPS 81
C. Rs. 450 d. Rs. 405

9. Durga sold a sofa set at Rs. 60000 for a profit of 20%.

CIalculate the cost price. b. Rs. 4800

a. Rs. 4500

C. Rs. S0000 d. Rs. 7200

10. What is the selling price of a bag of rice containing 50 kg, if

by costing at Rs.20 per kg a loss of 10% is made? S1okkgg7210000 DCP

a Rs.800 b. Rs. 900

C. Rs. 1050 d. Rs. 1200

11. Price of gas was first increased by 10% and then decreased

by 10%. What is the total change percent in price of gas?

a 0% b. 1% Catbtabo t

c, 2% 08d. 4% s lo lo t 7 1 t
0
s
12. A man sold a radio for Rs. 960 at 20% loss, find the cost ft
t
price of the radio.

a. Rs. 720 b. Rs. 1120 Sps CP LossY of CP

C. Rs. 1200 d. Rs. 1260 960 807 of CP

13. If 10% more than x is 550, what is x?

b. 50030i sa 605
TC. 525 abiotPs te9n 6818

of450 Xt lot X 550 1 lot of

14. Sapana allows a discount of 10% and still makes a profit of X s 550

d 20% on selling an article. If the market price of the article

is Rs.1200,find theactual profit. Sps Mp Discount

a. Rs. 120 1 b. Rs. 160 5888 20

C. Rs. 180 d. Rs. 240 Profitt

a
yh PÉfIx15. loot I spidxioot

Arun solda watch for Rs. 900 pays a profit of 12.5%. What

is the cost price?

a. Rs. 825 b. Rs. 800

C. Rs. 725 d. Rs. 700

16. A motor bike worth Rs, 150000 depreciates at the rate of

7.5% p.a. Find its value at the end of the year. wUI

a. Rs. 137850 01 b.Rs.145000 P PDo01t E T
c. Rs.138750
d. Rs.139125

150000 1 73

33

17. The price of kerosene inereases from Rs. 18 per liter to Rs.
Iyoa. 9%
20 per liter. What is the percentage increases.in price?

b. 9.11%

C. 10% d. 11.11% X loot

18. Ram buy a television for Rs. 30000 and sells it at a loss of
5%, what is the selling price?

a. Rs. 28500 b. Rs. 28000

C. Rs. 29500 d. Rs. 28250

19. fof incomeofKaranisRs1. 200, findof hisincome.

XX 1200
a. Rs. 1400 toy3b. Rs. 1500
d. Rs. 1800 sexy xx
C. Rs. 1600

20. A dealer gains the selling price of 10 radio sets by selling 60

sets. His percentage profit will be S P of 60 R CP of 60 R

a. 10% CP ooff 6120s2 Re I b. 15% s SP of 10 R
c. 20% CP 2.60
SP of 502 Rs Go
Purnima spot 12 st d. 25% SP OomffaGSkOiOnRgRSPaCoPfloOs1s0f26os0f LP of 6
Rs. sp
21. sold a caleulator for RRs.
375

25. What is her loss percentage? sst s Logxioot

a. 15% b. 6.25%

C. 7.14% d. 6.66% shoot

22. Suraj sold a watch for Rs. 525 making a profit of Rs.125.

What is his profit percentage? fit sÉsj xoo

a. 31.255% b. 25.25%

C. 19.23% d. 33.75%

23. Kalpana bought apples at Rs. 50 a dozen. She had to sell the

24. apples at a loss 4%. Find the selling price of an apple.
sp t b. Rs. 4.16 12 750 I 7 s 2
a Rs. 5

C. Rs.. 4 d. Rs. 63.60 SP CP Lost s P Loss7 of
s 964 of 2
Arjun makes a profit of 15% by selling a calculator for Rs.

FI575. What price did he buy it?
a. Rs.450 b. Rs. 500

C. Rs. 560 d. Rs.590

25. x% profit means an item costing Rs. 100 is sold at

a. 100bx b. 100x

c. 100+x d. 100-x

SP CP Profit 34

100 t XT Of 100

XXI 100 t 100 100 4

26. x% loss means an item costing Rs. 100 is sold at

a. 100/x b. 100x

C. 100 +x C. 100- x

27. We can compare profit or loss amount only on the basis of

a. SP b. CP

C. loss percent d. profit percent

28. Deepa makes a profit of 20% by selling a bag for Rs. 420.

EWhat price did she buy it? T
a. Rs. 350 b. Rs. 504
Rs. 400
C. Rs. 375 d.

29. At what price a fan should be sold at a gain of 15%, when it

was bought for Rs. 400? Tita

a. Rs.415 y b. Rs.430
C. Rs. 460
d. Rs. 340

30. The marked price of a radio is Rs. 500. If it is sold at a

discount of 25%, find the net selling price?

a. Rs. 350 b. Rs. 400

C. Rs. 425 d. Rs. 375

31. An institute allows 10% discounts in tuition fee on real fee.

What does a student pay for one subject tuition fee at Rs.

1200? b. Rs.ll100 RF 1200 1 1200

a. Rs. 1000 0

C. Rs. 1080 d. Rs. 1120

32. Deepika buys a watch for Rs. 4000 and sells it for Rs. 3600.
Find her loss percent.

a. 6% b. 10%

C. 12% d. 15%
gxop33. Whatisthevalueof , % ofRs.1.
a. Rs.7.5 b. 75 paisa Et loop
C. 7.5 paisa 0.75 paisa
7 sp
34. If 2/3 part of land cost Rs. 560. What will be the cost of 5/7

part of that same land?

a. Rs.600 b. Rs. 720

c. Rs. 960 d. Rs. 1440

35

Xs

3 I

XIII

35. Amrit buys a watch and sells it to Bharat at a profit of 10%.
Bharat sells it to Chandra at a gain of 20%. If Chandra
paid. Rs. 924 for it , what did Amrit pay for the watch?

a. Rs. 780 b. Rs.720

C. Rs. 700 d. Rs. 810

36. Babu buysa fan for Rs. 475 and sells it Rs. 500, find profit

%.

a. 5% b. 4.75%

C. 5.509% d. S.26%

Answers:

c 3. 5. b 6. b 7. b 8. c9. c L0. b

1. b 12. 13. b14. c 1S. b 16. d7, d 18.a 19. 20. C

21. b 22. a 23. c 24. b 25. c 26. c 27. b 28. a 29.c 30. d
31. 32. b 33. c 34. A 35. c 36. d

36

Chapter -6

INTEREST AND POPULATION GROWTH

Simple Interest: i. PP=T10*R0
V. A =P+I
i. PXTXR iiii.. RR==lPx1xT00
100

iv. TTp1x0R0 vi. P=A* 100
100 + TR

Compound Interest (C.

Compound Amount (C.A.)

Populationafter T years: P=

anIf R,% , R2 %, .... R% be rate of growth for the successive

year respectively, then population after "T" year is given by,

P;=P(o1+..(1+)

The value after T years at the rate of compound depreciation D

% per annum is : Pr D

100)

Objectives Questions

1, The interest on Rs 100 for 1 year is called..

a. principal b. time

C. amount d. rate

2. Express the rate in percentage per year if the rate of

interest is 1 paisa per rupee per month.

a. 1% b. 10%

C. 12% d. 100%

3. Find the simple interest on Rs 32500 in 6 years at 3% rate

of interest per annum.

a. Rs 2350 b. Rs 5850

c. Rs 8550 d. Rs 5580

37

4. Find the simple interest on Rs 4800 in 5 years at 6% per

annum.

a. Rs 1440 b. Rs 440

C. Rs 1220 d. Rs 1420

5. What sum of money must be invested at the interest of 4%

to give on interest Rs 900 in 5 years?

a. Rs 3500 b. Rs 2025

C. Rs 4500 d. Rs 4000

6. The simple interest on Rs 350 for 3 years at 8% per annum
is

a. Rs 82 b. Rs 84

C. Rs 88 d. Rs 80

7. Find simple interest of principal is Rs 600 in 5 years at the

rate 4%.

a. Rs. 120 b. Rs. 200

C. Rs. 130 d. Rs.150 fn noeoi

8. For how long must Rs 2500 be invested at 7 % per annum

to give Rs 750 simple interest?

a., 2 years b. 3 years
d. 5 years
C. 4 years

9 Find the simple interest on Rs1250 for 2 years at &% per

annum. b. Rs. 256.625
d. Rs. 296.265
a. Rs. 265.625
C. Rs. 265.265

10. According to the simple interest, if 'a' be the principle, "b'
be the time and 'e' be the rate, what will be the interest?

100 a+b+c
a. bc
b. 100

ab abc

c. 100c 100

11. If a certain sum of money doubles itself in 5 years, what is

ste the rate ofinterestperannum?

a. 20% b. 100%

C. 5% d. 10%

38

12. Find the simple interest on Rs 25000 for 2 years 8 months
25 days at 9%.

a Rs 6154.10 b Rs 8775

C. Rs S775 d. Rs 7785

13. If the interest of Rs 400 after 4 years is Rs 20, find the rate.

S/6% b. 6/5%

C. S/4% d. 7/5%

14. Ifa sum of money is doubled after 10years, find the rate.

a. 1% b. 10%

C. 12% d 20%

15. In what time will Rs 300 amount to Rs 405 at the rate of
4%?

35 36

a 2years b. 3 years

C. 345years 35

d. 3 years

16. Find the principal at the rate 5% for 6 years simple interest

is Rs 150.

a. Rs 400 b. Rs 450

C. Rs 550 d. Rs 500

17. According to símple interest, if x be the interest, y be the
time and z be the rate, what will be the principal?

100x b 100+ x 09

a. 100xyz 100xyz
100x
yz 100+ yz

d. 100x

18. According to the yearly compound interest, a sum of money

amounts to Rs. 1530 in 2 years and Rs 1545 in 3 years, what

was the sum?

a. Rs 1445 38it b. Rs1495 sit 2ec s

C. Rs 1500 d. Rsal520 o

19. Deepika borrowed Rs 1, 30,000 from Sonica at the rate of
21% P.a. How much S.I. will she have to pay at the end of l
year 6 months?

a. Rs 49050 b. Rs 40950

C. Rs 45900 d. Rs 94500

39

20. What is the rate of interest of a sum which doubles itself in

ns 20years?

a. 12% b 20%

C. 5% d. 10%

21. At what rate percent per annum will be the simple interest
of a sum will be half of the sum in 5 years?

12% b. 10%

c. 20% d. 50%

22. What is the interest of Rs 400 in 4 years at the rate of
1.25%?

a. Rs 15 b. Rs 30 rt

C. Rs 20 d. Rs 25

23. In how many years will the simple interest of a sum be 2/5

of the principal at 8%o p. a?

a. 4 years b. 5 years

C. 6 years d. 8 years

24. What principal will amount to Rs 4000 in 10 years at 2; %?

a. Rs 4S00 b Rs 3500
d. Rs 3000
C. Rs 3200

25. A sum ofmoneyinvested at 4o givesRs. 1 as interest per
TS I 361
day. Find the sum.

a. Rs 18000 P 3 b. Rs 12000 365 PYXI
d. Rs 6000
C. Rs 9000
YEI26. Find the rate of simple interest per annum if the principal issP

Rs 1375, whose amount becomes Rs 2035 in 2 years.

a. 6% b 12%

. 18% as d. 24%

27. In what time wll Rs 2500 Amount to Rs. 2575 at the rate of

4 %perannum?issdl

d. y

40

28. In how many yeat will a sum be tripled itself at the rate of
asae 25% p.a. simple interest?

a. 4 years b. 5 years

C. 8 years years

29. What is the amount of Rs 600 in S years at the rate of 4%?

a. Rs 720 b. Rs 630

c. Rs480 91s7 9h d. Rs 120

30. In what time the sum of money will triple at 8% p.a. simple

interest? PittZP s

a. 8 years b. 12 years

C. 20 years d. 25 years 2K Riot

31. To calculate simple interest, time must be converted into ..

a. day b. month

C. year d hour

32. After 3 years an interest of a sum of money will be Rs 275 at

S% p.a. Find the principal.

a. Rs. 1830 b. Rs. 1890

C. Rs1. 895 d. Rs. 1900

33. In what time Rs. 300 amount to Rs.285 at the rate of 4%?

a. syears b. 5 years

C. 4% years d. 4 years

34. What sum of money at the rate of 4% in 8 years gives an
Anterest of Rs 256?

a. Rs 800 b. Rs 40S

C. Rs 400 d. Rs 300

35. A sum of money amount to Rs. 1380 In 3 years and to Rs

1500 In 3 years. Find the rate of interest.

a. 20% 91 9b.5%
d 10%
C. 15%

41

36. Ifa sum ofmoneyincreasesby r ofitselfin 10years,what

is the rate is b. %

a%

d. %

37. If the interest in two years at the rate of 5% becomes Rs 20,

what is the principal? b. Rs 375 ieal
a Rs 500

c. Rs 300 d. Rs 200

38. Find the difference between simple interest and compound
interest of principal Rs 15000 at the rate of 10% p.a. for two
years.

a. Rs 1500 Ca b. Rs 150
601 d. Rs 14500
c. Rs 750

39. The present population of Sanga village is13310. How many
years ago was 10,000 if population growth rate is 10% p.a?.

a 2 years b. 3 years

c. 4 years d. 5 years

40. Find the compound interest on Rs 4000 for 1 year at 5% per

annum compounded half yearly.

(Hint: double the time and half the rate)

a. Rs 202.5 b. Rs 140

C. Rs 400 d. Rs 401

41. The population of a town was 40000 two years ago. Now the
population of the town is 44100. Find the growth rate of the

population?

a. 3% b. 4%

C. 5% d. 6%

42. The population of a town was 16500 three years ago. If it

had increased by 3%, 2.5% and 4%. In the last three years,

find the present population of the town? P Itf it it
a 008
a. 18000 b. 181167

C. 181176 d. 181170

43. A machine depreciates by the rate of 10% per annum. It

was purchased 3 years ago. If its present value is Rs 43740,

find its purchased price.

a. Rs 60200 b. Rs 60150

C. Rs. 60100 d. Rs 60000

42

44. Three years ago the population of a village was 40,000. If

the birth rate and death rate are 7% and 2% respectively,

find the present population of the village.

a. 34456 b. 36,570

C. 35,007 d. 46,30S

45. A machine costs Rs. 24,000. Calculate its value after one

year a 10% per annum compounded depreciation.

a. Rs.24,000 b. Rs.23,500

C. Rs.21,600 d. none

46 The population ofa village was 10,000 one year ago. The

population at present is 10,240, find the population growth

rate.

a. 2.5% b. 2.4%

C. 2.3% d. 2%

47. In how many years would an asset amounting to Rs 12500
be reduced to the value of Rs 64000 if the compound
depreciation is charged 20% p.a.

a. 3 years b. 4 years

C. 5 years d. 6 years

48. Subash bought a watch for Rs 5000 and sold it for Rs 625
after 3 years. Find the rate of compound depreciation of the

watch?

a. 30% b. 35%

c. 40% d. 50%

49. If the population of a town become 4 times in 2 years, What

is the rate of growth of population per year?

a. 2% b. 3% P Po it

C. 4% d. 5% Ufo To it E 2
I s 1 8 100
Answers: Just try

1.d 2.b 3.b 4.a 5.d 6.b 7.a 8.c 9.a 10.d

11.a 12.a 13.c 14.b 15.c 16.d 17.c 18.c 19.d 20.c

21.b 22.c 23.b 24.c 25.c 26.d 27.b 28.c 29.a 20.d

31.c 32.d 33.b 34.a 35.b 36.c 37.d 38.b 39.b 40.a

41.c 42.b 43.d 44.d 45.c 46.d 47.a 48.d 49.d

83

43

Chapter-7

MENSURATION

Triangle
Areaoftriangle = A bxh (forrightangledtriangle)

Area of triangle (A)=Vs(s - a)(s -b)(s -c), where a, b, c are the

sidesotfrianglaendS= 2, whereSissempei rimeter

Area ofequilateraltriangle (A) =a, where'a' is aside of the

riangle.

Quadrilateral 4 bhs dt

Areaoref ctangl(eA)=lx b n e

Perimeter of rectangle (P) = 2(1 + b),

Where, I and b are length and breadth of rectangle.

• Area ofsquare (A) = perimeter of square (P) = 41,

Where, I is the length of a side of the square.

Area ofparallelogram(A) =bxh

Areaotrfapezium(A)=(a+ b) xhsi

Where a and b are length of parallel sides and h be the distance

between parallel side.

Area ofrhomtbus(A) = (product of diagonals) = (d, x d,)

Area of quadrilateral (A) = (diagonal x sum of offsets)

-łdx (pı +pa)

Perimeter(P)=sumof length ofsides= a+b+c+d
Cuboids

Areaof floor (A) =1xb
Area ofceiling (A) = lxb

44

Area of four walls (A) = height of room x perimeter of floor
= 2h (1+ b)

Area of four walls, floor and ceiling = 2{h( + b) + lb}
Cube and cuboid

Total surfacearea of cube (TSA) = 6a
Total surfacearea oflidless cube (TSA) =5a

Volumeofcube(V) =a
Diagonalofcuboids =3 a

Total surfaceareaof cuboids (TSA) = 2(1b + Ih+ bh)

Volumeofcuboids ()=lxbxh=A x h,whereA =]xb

Diagonaol cf uboids= / +6 +R

Area of pathways
Area of path running outside rectangular field = 2d(l + b +2d)
Area of path running inside arectangular field = 2d(l + b- 2d)

Area of two intersection paths passing through the middle and
parallel to the side of the rectangular field
= d (l+ b- d), where , b and d are length breadth and width of
path.
Cost

Area of floor = Area ofcarpet

T= AC where A is area and C is the cost of per square unit
and T is the total cost

T= NC where N is number of bricks or stones, C is the cost of

per unit and T is the total cost.
T= IC where I is the length and C is the cost per unit length

Circle
Areaof circle (A) =
Circumference of circle (C) = 2rr

Sphere

Totalsurfaceareaofsphere (A) = 4nr =nd

Volumeosf phere(V) 4r=¿nd

Circumferenceof greatcircle =2rr

45

Total surfaceărea ofhemisphere (A) = 3nr

Volumeohfemisphere(V)-n

Note: TSA = CSA

Cylinder

Areaofbase(A) = r

Curvedsurfacearea(CSA) = 2rh

Total surfacearea (TSA) = CSA +2 (basearea)

= 2nrh+ 2r= 2r(r + h)
Volumeofcylinder (V)=h=A x h,

Prism

Lateral surfacearea (LSA) = Perimeter of base x height

Total surface area (TSA) =2A + lateral surfacesarea
(A is the area of base)

Volume(V)= A xh

Cones

Curvedsurfacesareaofcone(CSA) =rl

Areaofbaseofcone(A) =r

Totalsurfacesareaof thecone (TSA)=C.S.A +A

= Il +r=rl+)

A*hVolumeofcone(V) =1

P=f+h, where1=slantheight,h=heightofcone
Pyramid

The lateral surface area of pyramid= sum of areas of all its
triangular faces.

Area of each triangular face of a pyramid = base x sla
height

Total surface area=A+ lateral surface area

Volume (V) =A* h,where A is theareaofbase & hS the

height of pyramid.

46

Note: 10 millimeters (mm) =l centimeters(cm)

a) 10 centimeters (cm) =1 decimeters. (dm)
b)
c) 10 decimeters (dm) = 1 meter (m)

d) 10 meter (m) =1 decameters (dam)
10 decameters (dam) = I hectometer (hm)
e)
10 hectometer (hm) = 1 kilometer (km)
g)
I mile = 1.6093 km

Objective questions

1. The perimeter of the square is 36 cm. What is its area?

a. 81 cm b. 64 cm?

C. 72cm d. 324 cm2

2. The surface area of the rectangular box is 4128 cm and its

length and breadth are 36 cm and 24 cm respectively its

height is

a. 20 cm b 18 cm

C. 22 cm d. 16cm

3. The surface area of the cube is 216 cm, its volume is

a. 212 cm b. 36 cm

C. 216 cm d. 72 cm³

4. The volume of the sphere of diameter 2.1 cm is

a. 5 cm b. 4.851 cm

c. 4.52 cm d. 7.5 cm

5. The area of the circle is 154 em then the radius is

a. 1.5 cm b. 5 cm

C. 7 cm d. 14 cm

6. The cost of the carpeting a room at Rs. 50 per square meter
is Rs 1000, find the breadth of the room ifits length is 5 m

a 5r b. 4m

C. 6 mn d. 7 m

7. The perimeter of the rectangle of area 40 sq cm and length

8 cm is

a. 26 cm b. 28 cm

C. 16 cm d. 32 cm

47

8. If the total surface area of cube is 24 em“ then the area of

two faces of the cube is

a. 2 cm b. 3 cm²

C. 8 cm? d. 24 cm

9. A carpet is 80 em wide, what length of it is required to er

the floor of a room 8m long and 6m wide?

a 50 m b. 40 m

C 60n d. 80 m

10. Total surface area of a cylinder with height 10 cm and
diameter of the base 14 cm is

a. 748 cm b. 440 cm?

C. 478 cm d d. 784 cm

11. A piece of the copper wire 44 cm long is bent into the form
of a circle, the diameter of the circle is

a 14 cm b. 15 cm

C. 13 cm d. 13.5cm

12. The perimeter of the square is 10 cm. What is the area of
the square?

a. 2.5 cm? b. 62.5 cm
d. 0.625 cm?
c. 6.25 m?

13.

What will be the total cost for carpeting the roomn of 10 m

mlon?g and 4 m wide, if the cost of the carpet is Rs 8 per sq.

a. Rs 360 b. Rs 350

C. Rs 340 d. Rs 320

14. the
What is the diameter of a circle which has

circumference of 110 cm ?

a. 25 cm b. 30 cm
c. 35 cm d. 40 cm

15. The area of thesphere is 166 cm. Find its volume.
1372
b. 16
a. 3 Cm
cm
c. 31024 cm
id 11318em?

48

16 Find the curved surface area of a cone whose radius of a

base is 5 cm and slanting height is 7 cm.

a. 130 cm b. 120 cm

C. 110 cm? d. 100 cm

17. The perimeter of the square is 100 cm. Find the area of the

square. b. 125 cm

a. 625 cm

C. 1000 cm? d. 800cm?

18. What is the area of the rectangle whose length is 12 cm and
diagonal 13 em?

a. 144 cm? b 169 cm?

c. 60 cm d. 65 cm

19. What is the perimeter of the rectangle whose length is 4 cm

and diagonal 5cmn?

a. 14 cm .

b. 8 cm

C. 20 cm d. 18 cm

20. What is the length of the diagonal of the square of area 100

cm?

a 10 cm io b. 12 cm

c. Sy2 cm d. 20 cm

21. What is the perimeter of the square of area 169 sq cm?

a. 26 cm b. 13 cm

C. 52 cm d. 65 cm

22. What is the total length of the carpet required to cover the

floor of the room of8 m long and 6 m wide; if the carpet is 4

m wide?

a 32 m b. 24 m

C. 12 m d. 16 m

23. What is the cost of carpeting a room 8 m long, the breadth

being 75% of its length at the rate of 39 per square metre?

a. Rs 1865 b. Rs 1870

C. Rs1875 d. Rs 1872

24. How many pieces of carpet each 2.5 m wide and 8 m long

will be required to cover the floor of a hall 30 m long and 20

m wide?

a 50 b. 30

C. 60 d. 40

49