IQ Complete Notes

18. Flowers, Clothes White jfl} 4s k/LIff -cfO{=So"_ . . . . . 519

AB C D
D
19. Smokes, Lowers, Non smokers D
D
AB C

20. Human beings, Teachers, Graduate

AB C

21. Males, Father, Lawers

AB C

22. Nepies , Chinese , American

AB C D
23. Musicians, Men, Women

AB C D

24. Atmosphere, Nitrogen, Oxygen

AB C D

–

520 . . . . . c;O{ k/LIff bk{0f

25. Vegetable, Food, Carrot

AB C D
D
26. Truck, Goods, Ship

AB C

27. Oxygen, Air, Water

AB C D

28. Mineral, iron, Copper

AB C D
C D
29. Fruit, Pear, Grass

AB

30. Hen, Dog, Cat

A BC D

1. A Venn Diagrams: Answer Sheet
wife
husband 2. D ASIA
family Janakpur NEPAL

jf}l4s k/LIff -cfO{=So_" . . . . . 521

3. B Tree 4. A Chair
Animal Bed Furniture
Human
Family 6. D ck/fwL
5. C Daughter rf]/
Mother
Vehicle Gofolwz
7. A Truck
Jeep 8. C Men
Uncles Father

9. A House 10. A Hospital
Bedroom Bathroom Nurse Patient

11. D Mother 12. C Authors Teachers
Women Men
13. A Child
Cars 14. B Smokers Non smokers
Automobile
Motorcycle

Lawers

15. D 16. C Girl Student
Athetes
river
Perennial Cloths
White
sources of water
Human beings
canal Gradute

17. C Cricket players 18. B Flowers
Students
Table tennis fan

19. B smokers Non smokers 20.

Teachers

Lowers

–

522 . . . . . c;O{ k/LIff bk{0f

21. D Male 22. B Neplies
Father
Chinese
Lawers American

23. A Women 24. A
Nitrogen
Men

Musician Oxygen
Atmosphere

25. B Food 26. A Truck Ship
Carrot Vegetable

Goods

27. C Air 28. A Copper
Oxygen Iron Mineral
Water
29. D 30. B Hen
Peer
Fruit Dog
Cat
Grass

f) Matrices

Find the missing figures;

?

1. 2. (a) (b) (c) (d)

1 11 jf}l4s k/LIff -cfO={So_" . . . . . 523
2 22
?
2 22
4. (a) (b) (c) (d)
1 ?1
2
2
1
2 1 11
2 22
3. (a) (b) (c) (d)

? ?

5. (a) (b) (c) (d) 6. (a) (b) (c) (d)

? ?

7 . (a) (b) (c) (d) (a) (b)
(d)
8. (c)

–

524 . . . . . c;O{ k/LIff bk{0f

?

9. (a) (b) (c) (d) 10. (a) (b) (c) (d)
5. (b) 6. (b) 7. (b) 8. (b) 9. (a) 10.(d)
Answer Sheet: 3 (a) 4 (d)

1. (a) 2 (a)

g) Figure Formation and Analysis

lbPsf lrqx¿nfO{ hf]8]/ k"0f{ lrq agfpg'xf];\ .

Exercise-1
1.

(X) (a) (b) (c) (d)

2. (a) (b) (c) (d)

(X) (a) (b) (c) (d)

3.

(X)

4.

(X) (a) (b) (c) (d)

jfl} 4s k/LIff -cfO{=So"_ . . . . . 525

5.

(X) (a) (b) (c) (d)
6.

(X) (a) (b) (c) (d)
7.

(X)
8.

(X) (a) (b) (c) (d)
9.

(X)
10.

(a) (b) (c) (d)

(X) (a) (b) (c) (d)
11.
–
(X)

526 . . . . . c;O{ k/LIff bk0{ f

12.

(a) (b) (c) (d)

(X)
Answer Sheet

1.A 2.C 3.B 4.B 5.C 6.B 7.C 8. D 9.A 10.C
11.B 12.B

h) Construction of Squares and Triangles

EXERCISR -1

tn lbOPsf] lrq X ;uF A,B,C,D dWo] s'g ljsNk ldnfpbf ju{ aG5 ;xL ljsNk 5fGgx' f;] .

1.

(X) (A) (B) (C) (D)
2.

(X) (A) (B) (C) (D)
3. (A) (B) (C) (D)

(X)
4.

(X) (A) (B) (C) (D)

5.

(X) (A) (B) (C) (D)

6. (A) (B) jf}l4s k/LIff -cfO={So_" . . . . . 527
(A) (B)
(X) (C) (D)
7. (A) (B) (C) (D)
(A) (B)
(X) (A) (B) (C) (D)
8. (A) (B) (C) (D)
(A) (B) (C) (D)
(X) (A) (B) (C) (D)
9. (C) (D)
(C) (D)
(X)

10.

(X)

11.

(X)
12.

(X)
13.

(X)

–

528 . . . . . c;O{ k/LIff bk{0f

14.

(X) (A) (B) (C) (D)
15.

(X) (A) (B) (C) (D)

ANSWER SHEET -1
1.B 2.D 3.D 4.D 5.A 6.D 7.D 8.A 9.C
10.D 11.C 12.C 13.B 14.B 15.C

Type 2
EXERCISE -2

Tfn lbO{Psf A,B,C,D,E dWo sg' s'g lasNk ldndpbf lqe'h aG5 5gf6] ug'{xf;] .

1.

(A) (B) (C) (D) (E)

(a) ABC (b) ACE (c) BCD (d) BDE

2.

(A) (B) (C) (D) (E)

(a) BCD (b) ABC (c) CDE (d) BCE

3.

(A) (B) (C) (D) (E)

(a) ACE (b) ABD (c) BDE (d) CDE

4.

(A) (B) (C) (D) (E)

(a) ABC (b) ACE (c) BDE (d) CDE

jfl} 4s k/LIff -cfO{=So"_ . . . . . 529

5.

(A) (B) (C) (D) (E)

(a) ABD (b) ACE (c) ACD (d) CDE

6. (B) (C) (D) (E)

(A) (b) ABD (c) BDE (d) CDE

(a) ACE (B) (C) (D) (E)

7. (b) BCD (c) BDE (d) CDE

(A) (C)

(a) ABD (c) CDE

8.

(A) (B) (D) (E)

(a) BCD (b) ACD (d) BDE

9.

(A) (B) (C) (D) (E)

(a) ABE (b) BCE (c) ADE (d) BDE

10.

(A) (B) (C) (D) (E)

(a) ABC (b) BCD (c) CDE (d) BDE

EXERCISE -2 Answer Sheet

1. (d) 2. (b) 3. (d) 4. (d) 5. (b)

6. (a) 7. (b) 8. (c) 9. (d) 10. (c)

–

530 . . . . . c;O{ k/LIff bk{0f

3. Numerical Reasoning Test
a) Number Analogy

Ex 3:11 : : 7 : ?

a. 22 b. 29 c. 18 d. 51

clearly (3)2 + 2 = 11, Now (7)2 + 2 = 51 d. 56
d. 7
Exercise 1 d. 318
d. 625
1. 5 : 36 : : 6 : ? d. None
4. (d)
a. 48 b. 49 c. 50

2. 121 : 12 : : 25 : ?

a. 1 b. 2 c. 6

3. 25 : 125 : : 36 : ?

a. 180 b. 206 c. 216

4. 1 : 1 : : 25 : ?

a. 26 b 215 c 240

5. 49 : 81 : : 100 : ?

a. 64 b. 144 c. 169

1. (b ) 2. (c) 3. (c) 5. (b)

Exercise 2

Choose the similar alternative

1. Give Set : (9, 15, 21)

a. (10, 14, 16) b. (7, 21, 28) c. (5, 10, 25) d. (4, 8, 12)

2. Given set : (1, 8, 27)

a. (5,12, 32) b. (32, 39, 59) c. (60, 79, 86) d. (64, 125, 216)

3. Given set : (2, 14, 16)

a. (2, 7, 8) b. (2, 9, 16) c. (3, 21, 24) d. (4, 16, 18)

4. Given set (63, 49, 35)

a. (72, 40, 24) b. (72, 48, 24) c. (64, 40, 28) d. (81, 63, 45)

5. Given set (8, 3, 2)

a. (10, 6, 5) b. (63, 8, 3) c. (95, 24, 5) d. (168, 15, 4)

6. Given set: (81, 77, 69)

a. (56, 52, 44) b. (64, 61, 53) c, (75, 71, 60) d. (92, 88,79)

Answer Sheet

1( d) 2( d) 3( d) 4( d) 5(b ) 6(a)

jf}l4s k/LIff -cfO={So_" . . . . . 531

b) Classification/Odd One Out

Type 1 Choose the odd numbers which is different from the following alternatives

Examples

1. a. 13 b. 17 c. 23 d. 63 e. 71

Each of the number except 63 is a prime number. Hence and is (d)

Exercise 1

1. a. 17 b. 27 c. 29 d. 37 e. 59

2. a. 29 b. 53 c. 85 d. 125 e. 147

3. a. 37 b. 45 c. 49 d. 65 e. 79

4. a. 21 b. 39 c. 51 d. 63 e. 83

5. a. 126 b. 217 c. 345 d. 513 e. 730

6. a. 13 b. 17 c. 23 d. 37 e. 73

7. a. 57 b. 87 c. 131 d. 133 e. 143

8. a. 121 b. 137 c. 153 d. 177 e. 183

9. a. 27 b. 64 c. 125 d. 144

10. a. 10 b. 11 c. 15 d. 16

Answer sheet Exercise 1

1(b ) 2( d) 3(c ) 4( e) 5(c ) 6(c ) 7( c) 8( a) 9(d ) 10(b )

Type 2 Choose the number pair group which is different from other

Example 1

a. 50 - 66 b. 32 - 38 c. 64 - 80 d. 63 - 77

Clearly in each of the pair except (d), the each number is 16 move then the first.

Hence, ans (d).

Exercise 3

1. a) 21 : 24 b) 28: 32 c) 54: 62 d) 70 : 80

2. a) 4 : 16 b) 6 :42 c) 8:24 d) 17:54

3. a) 16 :64 b) 9 : 36 c) 36 : 216 d) 49 : 343

4. a) 7:26 b) 8:30 c) 10: 35 d) 13: 44

5. a) 15:63 b) 22: 91 c) 23 : 95 d) 31 : 97

6. a) 3 : 5 b) 6 : 2 c) 1 : 7 d) 7 : 3

7. a) (2, 3, 6) b) (6, 1, 6) c) (3, 3, 9) d) (6, 2, 5)

8. a) 7 - 84 b) 6 – 108 c) 5 - 75 d) 3 - 99

9. a) 21 - 49 b) 24 - 64 c). 25 - 54 d) 81 - 36

10. a) 1(9) 2 b) 3(243) 6 c). 5(854) 9 d) 4 (441) 7

–

532 . . . . . c;O{ k/LIff bk0{ f

Answer Sheet Exercise 2
1(c ) 2(d ) 3( b) 4( b) 5(d ) 6( d) 7( d) 8(a ) 9(c ) 10( d)

c) Insert the Missing Number

1. 7 2. ? 14 3. 594 198
? 15 5 10 ? 66
79
127 31 a) 11 b) 12
63 a) 2 b) 3 c) 22 d) 33
c) 6 d) 18
a) 190 b) 221

c) 236 d) 255 5. ? 8 6. ? 2
216 27 93
4. ? 1 125 64
82 74
53 55

a) 10 b) 12 a) 4 b) 305 a) 10 b) 11
c) 13 d) 15 c) 343 d) 729 c) 12 d) 13
5
7. 4 8. ? 9. 149 175
64 1 235 4

? 8 117 7 ? 203

a) 1 2 59 15 a) 148 b) 208
c) 3 25 29 c) 213 d) 233
a) 327
b) 2 c) 438 b) 386
d) 4 d) 469

10. ? 9 11. 0 7 12. 3 ?
? 26
22 13 6561 81
a) 45 b) 50
a) 38 b) 39 c) 60 d) 63 a) 9 b) 18
c) 40 d) 44 c) 24 d) 27

13. 4 9 9 16 16 ?

6 b) 25 12 20

a) 21 c) 35 d) 45

14. 18 19 22 24 26 27

35 43 ?
c) 89
a) 48 b) 76 d) 49
54 42 84
27 ? 42
15.

a) 12 9 b) 21 14 d) 35 7
16. 2 4 c) 24 1 7
39

20 90 ?
15
a) 20 b) 25 c) 50 d) 75
11 9
17. 4 3 6

144 9801 ?

- –

a) 1216 b) 2250 c) 8100 d) 11036
18. 12 8 16 7
25 21

80 207 ?
27
a) 184 b) 210 c) 241 d) 1425
30 45 18
19. 18 16 24 40
12

6 b) 9 8 ?
a) 6 c) 12 d) 18

20. ? 3 21. 3 15 22. 36 25
11 ? 27
22 5 2 ?
5 33 23
13 8 77 21 30
a) 5
c) 13 b) 12 a) 19 b) 22
d) 26 c) 32 d) 35

a) 1 b) 26
c) 45 d) 39

? 3 24. 3 15 47
23. 25.
2 25 441 6
406 5 5 1 64 3
11 27 ? 8
81 10 289 ? 13
a) 1 16 82
731
c) 1625 7 12 a) 0 b) 8
c) 125 d) 216
b) a) 25 b) 125
d) 2031 c) 156 d) 625

–

7 27. 13 28. 1
26. 63 ?

2 14 ?9 a) 10 1 15 ? 2 17
c) 12 42 16

30 3 5 46
3 18 5
15

a) 18 b) 33 8 19

c) 135 d) 145 b) 11 a) 13 b) 14
d) 13 c) 20 d) 21

29. T S
W 15 D
3

10 ?
J P

T G

a) 5 b) 9

c) 11 d) 13

1 1 1
30. 5 121 2 6 ?4

7 169 2

3 3 5
b) 246 2
a) 196 2 c) 250 d) 256 ?4
31. 2 3 2
48 3
2 4 384 6 d) 48
4
a) 42 b) 44 8
c) 46

-–

36 9 25
81 21 25 64 ? 144
32.
49 26 64

a) 19 25 16 d) 31 36
b) 23 c) 25
33. 25 49
100 25 25

6 100 25 5 81 25 4 25 36 ? 9

25 36 25 16

a) 2 b) 3 c) 4 d) 5 9
25
4
34.
16 361 1 64 289 16 1 ? 81

a) 260 81 9 d) 429 25
b) 269 c) 324 4
35.
5 2 6

9 12 10 8 8 3 ?7

a) 5 6 c) 17 4 d) 18 1
b) 9 3 1
36.
3 1 2 650 4 0 ?2

15010 5

a) 610 4 6 d) 690 8
37. 5 b) 660 c) 670 2

3 6 2 5? 2

12 4 5 18

2 3 9

- –

a) 15 b) 16 c) 17 d) 18
79 38 67
38. 93 27 16
37
63 42

3 b) 6 4 ?
a) 5 c) 8 d) 9

39. 5 19 3 75 64
? 29

4 6 5
c) 41
a) 25 b) 37 d) 47

40. 5 13 17
3 5 ?

4 12 15
a) 2 b) 6 c) 8
d) 64

41. 57
38 ?
48

4 2
c) 54
a) 27 b) 35 d) 64

42. 916 49 ?
34 23 15
d) 512
a) 125 b) 215 c) 251

43. 25 17 38 18 89 16
6 8 ?

- –

a) 13 b) 15 c) 17 d) 19
38 94
44. 5 4 24 11 ? 13
20 9 c) 36
91 d) 117
a) 26 b) 32 18 2 5 –2
c) 18 ? –3
45. 7 2
42 3 81 d) 30

a) –30 b) 13 ?

46.
84

14 12 18 9 16 11

a) 16 b) 21 c) 68 d) 88 6

47. 9 1 4 38 3
5 5 1

551 246 ?

3 6 4 7 92 4
6 8 3
a) 262 b) 622 d) 824
c) 631
48. 52 3
1 2 5

0

131 248 ?

2 44 8 7 1
6 9
a) 132 3 b) 262
c) 274 d) 320

-–

49. 5 3 6
2 4 2 34 7

584 694 ?

2 1 2 32 1 2
a) 678 2 1
b) 769 c) 824 16
15 d) 937 ?
50. 2 97
13
80 65

5 6 4 6 11 8

a) 35 b) 48 c) 72 d) 120

51. 5 7 18

6 93 15 9? 5 4 50 1

3 6 8

a) 5 b) 19 c) 27 d) 89
52. 101 43 48 34

38 56 ?
35 15 c) 158
184
a) 127 b) 142 4 d) 198

53. 2 8

4 C26 3 10 H70 5 6 J90 ?

5 4 6

a) 2 b) 3 c) 4 d) 5

54. 3 7 1
6 25 2 11 70 8 4 –12 5

4 6 ?

- –

a) 1 b) 2 c) 6 d) 10
2 4
55. 3
1 13 3
1? 51 17 5
d) 29 4
a) 21 5 c) 27 6 6
b) 25 8
56.
15 10 98 5 11 ? 8

14 8

a) 6 8 6 d) 12 4
b) 8 c) 9
57. 8
7 5 9

13 4 85 49 ? 4

a) 12 3 3 d) 18 3
27
58. b) 18 c) 15
4 65 8 ? 72
27 42

13 16 13 11

3 7 9

a) 6 b) 9 c) 12 d) 18

59. 11 44 16 40 ? 12
110 112 114

22 33 24 32 23 34

a) 35 b) 37 c) 45 d) 46

-

60. 3 5 4 7 3 5
51 4 ? 5
39 3
6 5 5

a) 35 b) 37 c) 45 d) 47
61.
5 3 2 7 6 7
63 8 41 9 ? 5

6 3 8

a) 26 b) 82 c) 83 d) 86
62.
26 35 2 3
? 5
168 2 120 1
3 2 4

a) 84 b) 195 c) 240 d) None of these
63.
466 398
341 282

250 ?

a) 232 b) 268 c) 298 d) 350

Answer Missing Number

1. d. 7 × 2 + 1 = 15, 15 × 2 + 1 = 31, 31 × 2 + 1 = 63, 63 × 2 + 1 = 127
127 × 2 + 1 = 255

2. d. We have, 5 × 2 = 10, 7 × 2 = 14
So, missing Number = 9 × 2 = 18

3. c. We have,
594  3 = 198
198  3 = 66
So, missing number = 66  3 = 22

4. c. We have,
1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8
So, missing number = 5 + 8 = 13

5. c. We have,
Moving clockwise = 23, 33, 43, 53, 63…
So, missing number = 73 = 343

6. b. We have,
Right half from the series 2, 3, 4, 5
Left half from the series 5, 7, 9, 11
So, the missing number = 11

7. a. l;wf /]vfsf] bO' { 5p] df gDa/ / To;sf] ju{ ;V+ of /xs] f 5g\ .

So, the missing number = 12 = 1

8. d. We have,
4×2–1=7
9. d. 7 × 2 + 1 = 15
10. a. 15 × 2 – 1 = 29
11. d. 29 × 2 + 1 = 59, 59 × 2 – 1 = 117, 117 × 2 + 1 = 235,
12. a. So the missing number = 235 × 2 – 1 = 469
13. b. We have,
14. d. 149 + 26 = 175
175 + 28 = 203
So, the missing number = 203 + 30 = 233
We have,
9 + 22 = 13
13 + 32 = 22
So, the missing number = 22 + 42 = 38.
We have,
Moving clockwise, 13 – 1, 23 – 1, 33 – 1
So, the missing number = 43 – 1 = 63
We have,
Moving clockwise, 3, 32 = 9, 92 = 81, 812 = 6561
So, the missing number = 32 = 9
We have,

4× 9=6

9 × 16 = 12

So, the missing number 16 × x = 20, x = 5 , x = 25
We have,
(18 + 19) – 2 = 35
(22 + 24) – 3 = 43

–

So, the missing number (26 + 27) – 4 = 49

15. b. We have,
16. c.
17. c. (9 × 3 = 27) (9 × 6 = 54)
18. a.
19. b. (14 × 3 = 42) (14 × 6 = 84)
20. c.
So, the missing number is 7 × 3 = 21
21. a.
22. a. We have
23. d. 22 + 42 = 20
33 + 92 = 90
So, the missing number is 12 + 72 = 50

We have,
4 × 3 = (12)2 = 144
11 × 9 = (99)2 = 9801
So, the missing number is 15 × 6 = (90)2 = 8100

We have,
(12)2 – (8)2 = 80
(16)2 – (7)2 = 207
So, the missing number is (25)2 – (21)2 = 184

We have,

12, 18, 30 ;a} tnsf] ;+Vof 6 sf u'0fg ;V+ of xg' \ .

16, 32, 40 ;a} tnsf] ;+Vof 8 sf u'0fg ;V+ of xg' \ .

So, the missing number is 36, 18, 27 ;a} 9 sf u0' fg ;+Vof x'g\ .

We have,
3×2=6–1=5
5 × 2 = 10 – 2 = 8
8 × 2 = 16 – 3 = 13
13 × 2 = 26 – 4 = 22
So, the missing number is 22 × 2 = 44 – 5 = 39

We have,

3×2+1=7

5 × 2 + 1 = 11

7 × 2 + 1 = 15

So, the missing number is 2 × 2 + 1 = 5

We have,

27 b]vL ;'? u//] Ps Ps :6k] 5f]8/] Pp6f Series a9s] f] 5, 27, 30, 33, 36
To;} u/L csf]{ Series ? , 21, 23, 25 n] a9s] f] 5 .

So, the missing number is 19

We have,

3 × 5 + 1 = 16 –

-

24. d. 16 × 5 + 1 = 81
25. d. 81 × 5 + 1 = 406
26. c. So, the missing number is 406 × 5 + 1 = 2031
27. c. We have,
28. b. (2 + 3)2 = 25
29. b. (15 + 6)2 = 441
30. d. (10 + 7)2 = 289
31. d. So the missing number is (12 + 13)2 = 625
We have,
(5 – 4)3 = 1
(7 – 3)3 = 64
(11 – 8)3 = 27
So, the missing number (8 – 2)3 = 216

We have

7 × 2 = 14

2 × 15 = 30

9 × 7 = 63
So, the missing number (15 × 9) = 135

We have,

5+3=8

8 + 4 = 12

12 + 1 = 13

So, the missing number is 12

We have,

;uF }sf] ;fgf] / glhssf] 7n" f] ;V+ of afxL/ leq u//] /flvPsf] 5 x/]s k6s Ps rf6] L ;fgf] afxL/ csf]{ rf6] L
7n' f] afxL/ u/]/ .

So, the missing number is 14.

We have,
W–T=3
S – D = 15
T – J = 10
So, the missing number is P – G = 9

We have
(1 + 2 + 3 + 7)2 = 169
(1 + 2 + 3 + 5)2 = 121
So, the missing number is (1 + 4 + 5 + 6)2 = 256

We have

2 × 3 × 4 × 2 = 48

-–

8 × 6 × 4 × 2 = 384

So, the missing number is (2 × 2 × 3 × 4) = 48

32. d. We have

49 + 36 + 64 = 26

9 + 25 + 81 + 16 = 21

So, the missing number is 25 + 144 + 64 + 36 = 31

33. c. We have,

100 + 100 + 25 + 25
5 =6

25 + 25 + 36 + 81
5 =5

49 + 9 + 16 + 36
So, the missing number is 5 = 4

34. c. We have
35. a.
36. d. ( 25 + 16 + 1 + 81 )2 = 361
37. d. ( 64 + 4 + 16 + 9 )2 = 289
So, the missing number is ( 9 + 81 + 25 + 1 )2 = 324
We have,
(12 + 5) – (6 + 2) = 9
(10 + 8) – (6 + 4) = 8
So, the missing number is (7 + 3) – (4 + 1) = 5
We have
52 + 32 + 42 + 12 = 51 × 10 = 510
32 + 42 + 62 + 22 = 65 × 10 = 650
So, the missing number is 82 + 22 + 12 + 02 = 69 × 10 = 690
We have,
5×4 ×3×2

10 = 12

6×5×3×2
10 = 18

So, the missing number is 9×5×2×2
10 = 18

38. d. We have,
39. c. 93 – (27 + 63) = 3
79 – (38 + 37) = 4
So, the missing number is 67 – (16 + 42) = 9

We have,

(5 × 3) + 4 = 19

- –

40. c. (6 × 4) + 5 = 29
41. b. So, the missing number is (7 × 5) + 6 = 41
42. a. We have,
43. b. 52 – 42 = 32
132 – 122 = 52
44. c. So, the missing number is 172 – 152 = 82
45. d. We have
46. d. 8×3×4
47. b.
2 = 48
7 × 5× 2

So, the missing number is 2 = 35

We have,
32 = 9, 42 = 16, = 916
22 = 4, 32 = 9, = 49
So, the missing number is 12 = 1, 52 = 25,= 125
We have,
25 + 17

7 = 6,
38 + 18

7 =8
89 + 16

So, the missing number is 7 = 15

We have,
5 + 4 = 9, 5 × 4 = 20
3 + 8 = 11, 3 × 8 = 24
So, the missing number is 9 + 4 = 13, 9 × 4 = 36
We have
7 × 2 × 3 = 42
9 × 1 × 2 = 18
So, the missing number is 5 × (-2) × (-3) = 30
We have
14 × 12 18 × 9

2 = 84, 2 = 81

16 × 11
So, the missing number is 2 = 88

We have,
915 – 364 = 551
789 – 543 = 246
So, the missing number is 863 – 241 = 622

- –

48. b. We have,
49. a. 2 –1 = 1 , 6 – 3 = 3, 5 – 4 = 1 (131)
50. b. 4 – 2 = 2, 6 – 2 = 4, 8 – 0 = 8 (248)
51. d. So, the missing number is (262)
52. b. We have,
53. c. 5 × 1 = 5, 4 × 2 = 8, 2 × 2 = 4 (584)
54. b. 3 × 2 = 6, 3 × 3 = 9, 2 × 2 = 4 (694)
55. d. So, the missing number is 6 × 1 = 6, 7 × 1 = 7, 4 × 2 = 8 (678)
56. a. We have
57. a. (15 – 5) × (6 + 2) = 80
(9 – 4) × (7 + 6) = 65
So, the missing number is (13 – 11) × (16 + 8) = 48
We have,
(15 × 5) + (6 × 3) = 93
(18 × 1) + (4 × 8) = 50
So, the missing number is (7 × 5) + (9 × 6) = 89
We have
(101 + 15) – (43 + 35) = 38
So, the missing number is (184 + 48) – (34 + 56) = 142
We have
(2 + C + 5) × 3 – 4 = 26
(4 + H + 4) ×5 – 10 = 70
So, the missing number is (8 + J + 6) × 4 – 6 = 90
We have
(32 + 62) – (22 + 42) = 25
(72 + 112) – (62 + 82) = 70
So, the missing number is (42 + 12) – (52 + 22) = –12
We have,
(5 × 2) + (3 × 1) = 13
(3 × 4) + (5 × 1) = 17
So, the missing number is (6 × 4) + (5 × 1) = 29
We have,
(10 – 8) × (15 – 8) = 14
(8 – 6) × (9 – 5) = 8
So, the missing number is (6 – 4) × (11 – 8) = 6
We have,
(7 × 4) – (5 × 3) = 13

-–

(8× 4) – (9 × 3) = 13
So, the missing number is (9 × 4) – (8 × 3) = 12

58. a. We have
59. c. (27  3) + (16  4) = 13
60. c. (42  7) + (65  13) = 11
61. b. So, the missing number is (27  9) – (72  8) = 6
62. b. We have
63. a. (11 + 44 + 33 + 22) = 110
(16 + 40 + 24 + 12) = 112
So, the missing number is (12 + 34 + 23 + 45) = 114
We have,
(6 × 5) + (3 × 3) = 39
(7 × 5) + (4 × 4) = 51
So, the missing number is (5 × 5) + (3 × 5) = 40
We have,
(6 × 8) + (5 × 3) = 63
(9 × 3) + (7 × 2) = 41
So, the missing number is (8 × 5) + (6 × 7) = 82
We have,
(6 + 2 + 2 + 3)2 – 1 = 168
(5 + 3 + 2 + 1)2 – 1 = 120
So, the missing number (2 + 3 + 4 + 5)2 – 1
(466 – 341) × 2 = 250,
So, (398 – 282) × 2 = 232

d) Common Property

o; ks| f/sf] kZ| gdf lbOPsf k|Zgsf] ks| [lt x]/L ;f]xL k|s[ltsf] ljsNk dWo] 5gf}6 ug{k' 5{ .

Exercise 1

1. (5, 25) (b) (9, 27) (c) (4, 64) (d) (6, 216)
(a) (9, 81) (b) (4, 8, 64)
(b) (64, 36, 16) (c) (3, 9, 27) (d) (4, 16, 48)
2. (2, 4, 8)
(a) (3, 9, 36) (c) (36, 24, 11) (d) (81, 72, 15)

3. (49, 25, 19)
(a) (40, 26, 12)

4. (9, 25, 49)

-–

(a) (36, 49, 81) (b) (121, 169, 225) (c) (81, 64, 36) (d) (100, 81, 64)

5. (2, 4, 8, 16)

(a) (4, 8, 16, 64) (b) (6, 36, 216, 108) (c) (5, 25, 125, 250) (d) (3, 9, 27, 81)

6. WVU, EDC, LKY h:t} tnsf] s'g ldN5 <

(a) GHF (b) BAZ (c) PON (d) WUT

7. DFH, RTV, JLN, VXZ ;uF ;dfg lx;fan] tnsf] dWo] sg' lsnKk ldN5 <

(a) ACD (b) NPQ (c) CFI (d) OQS

8. 6f]kL, Åof6 / ku/L h:t} tnsf] s'g ldN5 < (c) ;'/Iff (d) 5ftf

(a) skfn (b) x]Nd]6

9. 10, 40, 160 ;Fu ldNbf] ljsNk sg' xf] <

(a) (5, 20, 160) (b) (5, 20, 80) (c) (5, 20, 90) (d) (5, 30, 80)

10. (343, 49, 7_ h:t} tnsf] sg' ljsNk ldN5 <

(a) (72, 12, 2) (b) (98, 14, 2) (c) (36, 12, 4) (d) 128, 32, 8

11. (700, 70, 7) ePh:t} tnsf] s'g ljsNk ldN5 <

(a) (500, 50, 10) (b) (600, 60, 6) (c) (1200, 600, 300) (d) (150, 90, 9)

12. ufO,{ ss' '/ / lj/fnf] h:tf} sg' xf] ?

(which of the following is like cow, dog and cat?)

(a) e;+} L (Buffalo) (b) 3f8] f (Horse) (c) afvf| (Goat) (d) dflysf ;a} (Above all)

Answer Sheet

1. a 2. c 3. b 4. b 5. d 6. c 7. d 8. b 9. b 10. b 11. b 12. d

e) Matrices

1. 6 6 8 2. 26 18 10 3. 1 4?
5 75 4 25
11 9 7 2 23
49 64 169
4 3? 541
(a) 3 (b) 4
120 126 320 10 5? (c) 5 (d) 6

(a) 4 (b) 8 (a) 2 (b) 4
(c) 12 (d) 16 (c) 5 (d) 6

4. 1 4 9? 5. 5 5 2 6. 28 60 48
1 2 34 2 41 5 67

2 4 6? 8 3 10 14 39 27

(a) 16, 8 (b) 25, 5 40 30 ? 7 ? 16
(c) 36, 4 (d) 49, 7
(a) 10 (b) 12 (a) 18 (b) 23
(c) 13 (d) 20 (c) 24 (d) 27

-–

7. 5 6 7 8. 3 68 9. 3 4 5
3 45 5 84 3 7 12
4 7?
9 10 11 3 ? 22
(a) 6 (b) 7
345 460 ? (c) 8 (d) 9 (a) 11 (b) 10
(c) 9 (d) 8
(a) 535 (b) 577
(c) 755 (d) 775

10. 85 20 5 11. 7 9 21 27 12. 12 (47) 21
126 24 6 4 2 36 18 10 (52) 4
175 ? 7 9 4 54 ? 64 (?) 24

(a) 22 (b) 24 (a) 18 (b) 24 (a) 16 (b) 40
(c) 26 (d) 28 (c) 36 (d) 58 (c) 62 (d) 83

13. 9 A 12 14. A DH 15. A DG
B 10 7 F IM D IN
? NR I P?
8 C 11
(a) K (b) N (a) V (b) W
(a) A = 13, B = 11, C = 9 (c) O (d) P (c) X (d) Y
(b) A = 13, B = 9, C = 11
(c) A = 9, B = 11, C = 13 WO
(d) A = 9, B = 13. C = 11 JK
M?
16. Z ?S 17. F 18. H K Q
R O? A (b) X C GO
E (d) P EJ?
? GC T?
(a) N QS
(a) WJK (b) KWT (c) D NR (a) T (b) P
(c) WKJ (d) JKW (b) L (c) N (d) L
20. P (d) U
19. O 21. A M BN
BGN M R C SD

DJ R (a) I E U F?
(c) O
GN? (a) G (b) R
(c) T (d) V
(a) U (b) V
(c) W (d) X

-–

22. 2 5 10 23. 16 210 14 24. 23 529 1024
17 ? 87 14 156 12 21 441 144
50 65 82
12 ? 10 19 361 ?
(a) 20 (b) 26
(c) 27 (d) 32 (a) 90 (b) 100 (a) 1441 (b) 3529
(c) 110 (d) 120 (c) 8281 (d) 9861

25. 2 2 256 26. 1 3 7 27. 7 4 5
3 2? 8 76
5 12 14 3 3?
29 19 31
4 2 46656 25 ? 28

(a) 2765 (b) 3125 125 192 56
(c) 8796 (d) 80008
(a) 64 (b) 56 (a) 3 (b) 4
(c) 48 (d) 40 (c) 5 (d) 6

28. 24 144 384 29. 11 17 58 87 30. 42 44 38
6 36 ? 23 55 28
88 19 61 56

2 12 32 91 22 70 50 37 ? 39

1 6 16 10 142 11 ? (a) 22 (b) 33
(c) 66 (d) 77
(a) 80 (b) 85 (a) 3 (b) 6
(c) 91 (d) 96 (c) 7 (d) 9

31. 1 79 32. 8 17 33 33. 1 23
2 14 ? 12 5 29 11 75
120 45 ?
3 105 117 10 13 ?
(a) 19 (b) 17
(a) 26 (b) 20 (a) 9 (b) 23 (c) 16 (d) 15
(c) 16 (d) 12 (c) 33 (d) 43

34. 963 2 844 35. 188 300 263
464 ? 903 893 ? 915

(a) 1 (b) 2 (a) 88 (b) 96
(c) 3 (d) 4 (c) 238 (d) 500

Answer Sheet (Matrix)

1. b We have

- –

(6 × 5 × 4) = 120

(6 × 7 × 3) = 126

So the missing number is (8 × 5 × 8) = 320

2. a We have
3. c
4. a (10 + 5 + 11) = 26
5. a
6. d (5 + 4 + 9) = 18

7. b So the missing number is (7 + 1 + 2) = 10

8. a We have,
9. b (1 + 4 + 2)2 = 49
10. d (4 + 2 + 2)2 = 64
11. b So the missing number's (5 + 3 + 5)2 = 169
(1)2, (2)2, (3)2, (4)2 = 16

2, 4, 6, 8

We have,

(8 × 5 × 2) (5 × 4 × 3)
2 = 40 , 2 = 30

(2 × 1 × 10)
So the missing number is 2 = 10

We have,
(48 – 28) × 3 = 60
(7 – 5) × 3 = 6
(27 – 14) × 3 = 39
So the missing number is (16 – 7) × 3 = 27

We have,

5 × 9 = 45 ljrdf ePsf] 3 nfO{ cufl8 /fVg] = 345

6 × 10 = 60 lardf ePsf] 4 nfO{ cufl8 /fVg] = 460

So the missing number is

7 × 11 = 77 lardf ePsf] 5 nfO{ cufl8 /fVbf = 577

We have

(5 + 3) (6 + 8)
2 = 4, 2 = 7,

(8 + 4)
So the missing number is 2 = 6

We have

3 + 4 = 7, 3 + 4 + 5 = 12

So the missing number is 3 + 7 = 10,

We have,

85 + 3 = 20, 126 + 3 = 24,
5 6

So the missing number 1775 + 3 = 28

We have

- –

12. d 7 × 3 = 21, 9 × 3 = 27
4 × 9 = 36, 2 × 9 = 18
13. d So the missing number is 9 × 6 = 54, 4 × 6 = 24
14. a We have,
15. b 12 21
16. c 3 = 4, 3 = 7, = (47),
17. c 10 4
18. a 2 = 5, 2 = 2 = (52)

64 24 –
So the missing numbr is 8 = 8, 8 = 3 = (83)

We have
(9 + 9 + 12) = 30
(13 + 10 + 7) = 30
So the missing number is (8 + 11 + 11) = 30
We have,
D+5=I+5=N
H+5=M+5=R
So the missing Alphabet is A + 5 = F + 5 = K,
We have
A + 3 = D, D + 3 = G
D + 5 = I, I + 5 = N
So the missing Alphabet is I + 7 = P, P + 7 = W
We have
Z – 8 = R, R – 8 = J
G + 8 = 0, 0 + 8 = W
S – 8 = K, K – 8 = C
 WKJ
We have,
Putting A = 1, B = 2, C = 3 ……. Z = 26
F–A=6–1=5=E
W – J = 23 – 10 = 13 = M
O – K = 15 – 11 = 4 = D
Putting A = 1, B = 2, C = 3……. Z = 26
We get the given matrix

8 11 17
3 7 15
5 10 ?
Here,
2 × (11 – 8) = (17 – 11)
6=6
So, 2 × (10 – 5) = (x – 10)
10 = 20 – 10 = 10

-

19. c  20 = T
We have,
20. B + 5 = G, G + 7 = N
21. d D + 6 = J, J + 8 = R
22. b So the missing Alphabet is G + 7 = N, N + 9 = W
23. c
A + 1 = B, M + 1 = N
24. c R + 1 = S, C + 1 = D
E + 1 = F, U + 1 = V
25. b We have, (12 + 1), (22 + 1), (32 + 1), (42 + 1) (52 + 1) = 26
We have,
26. c (16 × 14) – 14 = 210
(14 × 12) – 12 = 156
27. c So the missing number is (12 × 10) – 10 = 110
We have,
28. d (23)2 = 429, (32)2 = 1024
(21)2 = 441, (12)2 = 144
29. c So the missing number is (19)2 = 361, (91)2 = 8281
We have,
30. a 2 + 2 = 4 = 44 = 256
4 + 2 = 6 = 66 = 46656
So the missing number is 3 + 2 = 5 = 55 = 3125
We have,
1×5 = 5, 5 × 5 = 25, 25 × 5 = 125
7 × 2 = 14, 14 × 2 = 28, 28 × 2 = 56
So the missing number is 3 × 4 = 12, 12 × 4 = 48, 48 × 4 = 192
We have,
(7 × 3) + 8 = 29
(4 × 3) + 7 = 19
So the missing number is (5 × 5) + 6 = 31
We have,
1 × 2 = 2, 2 × 3 = 6, 6 × 4 = 24
6 × 2 = 12, 12 × 3 = 36, 36 × 4 = 144
So the missing number is 16 × 2 = 32, 32 × 3 = 96, 96 × 4 = 384
We have
(11 + 88 + 91 + 10) = 200
(17 + 19 + 22 + 142) = 200
So the missing number is (87 + 56 + 50 + 7) = 200
We have
(42 – 38) × 11 = 44
(28 – 23) × 11 = 55
So the missing number is (39 – 37) × 11 = 22

-–

31. d We have
32. c (1 × 2) + 1 = 3
33. c (14 × 7) + 7 = 105
34. b So the missing number is ( 9 × 12) + 9 = 117
35. a
We have
(8 × 2) + 17 = 33
(12 × 2) + 5 = 29
So the missing number is (10 × 2) + 13 = 33

We have
(11)2 – (1)2 = 120
(7)2 – (2)2 = 45
So the missing number is, (5)2 – (3)2 = 16

we have,
(9 + 6 + 3) – (8 + 4 + 4) = 2
(4 + 6 + 4) – (9 + 0 + 3) = 2

We have
(263 – 188) × 4 = 300
So the missing number is (915 – 893) × 4 = 88

f) Data Checking/Verification

-tYofªs\ hfrF ÷?h'_

Type 1:

tn lbOPsf ljsNkx?nfO{ ljleGg tl/sfn] ldnfOPsf] XG' 5 . sg' } bO' {j6f ljsNkx? p:t} xG' 5g\ . k|Zgdf lbOP
adfl] hdsf hf8] f ePsf] ljsNknfO{ 5gf}6 ug'k{ g]{ xG' 5 .

1. (a) 1 R Q a (b) R 1 a Q (c) 1 r q a (d) 1 R Q a

(i) a & b (ii) b & d (iii) a & d (iv) None of these

2. (a) M B 2 1 (b) b 2 m 1 (c) 1 M 2 B (d) b 2 m 1

(i) a & b (ii) c & b (iii) a & d (iv) b & d

3. (a) A B c (b) A b C (c) A B C (d) B a C (e) A B C

(i) a 7 e (ii) b & d (iii) b & c (iv) c & e

4. (a) 1 3 5 B (b) 1 3 5 B (c) b 5 3 1 (d) 5 1 3 B (e) 3 5 B 1

(i) a & b (ii) c & d (iii) b & e (iv) None of these

5. (a) A a B b (b) B b A a (c) a b A B (d) B A b a (e) a b A B

(i) a & b (ii) b & c (iii) c & d (iv) c & e

6. (a) 2 5 P R (b) R 5 P 2 (c) 2 5 P R (d) R P 5 2 (e) 2 P R 5

(i) a & b (ii) a & c (iii) d & e (iv) None of these

7. (a) Z 1 Y r (b) R 1 Z Y (c) 1 Y Z R (d) R 1 Z Y (e) Z Y R 1

(i) a & b (ii) b & c (iii) b & d (iv) d & e

8. (a) 1 2 3 T (b) T 2 3 1 (c) 2 3 T 1 (d) T 2 3 1 (e) 3 1 T 2

- –

(i) b & d (ii) a & b (iii) d & b (iv) d & e (e) E 8 D B
9. (a) 8 b D E (b) D 8 E b (c) D 8 E b (d) b E D 8 (e) a d c b
(ii) b & d (iii) c & d (iv) d & e
(i) b & c (b) c d b a (c) b c d a (d) b c d a
10. (a) a b c d (ii) b & c (iii) c & d (iv) d & e

(i) a & b

Type 2:

tnsf kT| os] kZ| gdf lbOPsf 4 ljsNkx? dWo] 3 j6f cz4' 5g\ / Pp6f z'4 5 . pQm z'4 ljsNk 5gf}6 ugx{' f];\ .

11. (A) Ps ;o rfln; (B) Ps rfln; ;o (C) 1 ;o 40 (D) 1 ;o rfln;

12. (A) 2345 (B) 23,45 (C) 2,345 (D) 234,5

13. (A) School (B) Schoool (C) Schol (D) Schoohl

14. (A) Two Hundred Fifty Five (B) Two Hundered Fifety Five

(C) Two Hundred Fivety Five (D) Two Hundred Fifty Fives

15. (A) 5 ;o 40 (B) 5 ;o rfln; (C) kfFr 100 rfln; (D) kfFr ;o rfln;

Answer Sheet (Data Checking)

1. iii 2. iv 3. iv 4. i 5. iv 6. ii 7. iii 8. i 9. i 10. iii

11. A 12. C 13. A 14. A 15. D

g) Height and Distance, Time and Work, Loss and
Profit

Height and Distance

Values of T-ratios 0o 30o 45o 60o 90o
θ 0 1 1
1 2 3
sinθ 1 2 2 0
1 1
cosθ 0 3 2 2 Not defined
2
tanθ 1 3
1
3

Trigonometrical Identities: B
i) sin2θ + cos2θ = 1
ii) 1 + tan2θ = sec2θ h p
iii) 1 + cot2θ = coses2θ A

O 0
b

Important formulae

i) sinθ = Perpendicular = AB ii) cosθ = Base = OA
Hypotenous OB Hypotenous OB

-–

ii) tanθ = Perpendicualr = AB
Base OA

Exercise 1

1. 1.6 cUnf] Pp6f dfG5]n] 20m k/ /x]sf] :tDesf] 6'Kkfd] f x]bf{ 45o pGgtf+z sf]0f aG5 eg] :tDesf] prfO{ kQf nufpg'xf];\ .

a) 21.6 b) 18.4 c) 22.6 d) 19.6

2. gbLsf] Ps lsgf/fdf 20m cUnf] 6fj/ 5 / gbLsf] csf{] lsgf/faf6 6fj/sf] 6'Kkf]df xb] f{ pGgtf+z sf]0f 30o /x]5 eg]
gbLsf] rf}8fO{ kQf nufpgx' f];\ .

a) 20 3 m b) 15 3 c) 10 3 d) 25 3

3. 6m cUnf] 3/sf] 5fgfaf6 66m cUnf] dlGb/sf] 6K' kfd] f xb] f{ pGgtfz+ sf0] f 60o kfOof] eg] 3/ / dlGb/ aLrsf] b/' L kQf

nufpg'xf;] \ .

a) 20 3 b) 15 3 c) 10 3 d) 18 3

4. 1.5m cUnf] dflg;n] rf}/df /xs] f] Pp6f vDafaf6 150m sf] b/' Ldf pleP/ vDafsf] 6'Kkfd] f xb] f{ 45o sf] pGgtfz+ sf]0f

kfP5 eg] vDafsf] prfO{ kQf nufpg'xf;] \ .

a) 151.5m b) 48.5m c) 552.5m d) 153.5

5. Pshgf dflg;n] rªu\ f p8fO/xs] f] lyof] . olb wfuf]sf] nDafO{ 300m lyof] / o;n] lIflth;uF 45o sf] sf0] f agfPsf]

lyof] eg] rª\uf lIflthaf6 slt prfO{df pl8/xs] f] lyof] <

a) 150 2 b) 100 2 c) 135 2 d) 140 2

6. Pp6f dflg;n] cfk"meGbf cufl8sf] 52m cUnf] vDafsf] 6'Kkf]df xb] f{ pGgtf+z sf]0f 30o kfP5 . olb dflg; / vDafaLrsf]

b/' L 86m 5 eg] To; dflg;sf] prfO{ kQf nufpgx' f;] \ .

a) 2.34m b) 3.34m c) 2.9m d) 2.28m

7. 1.75m dL cUnf] sg' } Pp6f dfflg;n] cfÇgf] cufl8 /x]sf] Pp6f vDafsf] 6K' kf]nfO{ 45o sf] pGgtf+z sf0] f kfP5 . olb

vDaf dflg;af6 18.25 ld= 6f9f lyof] eg] vDafsf] prfO{ kQf nufpg'xf];\ .

a) 18.25m b) 19.25m c) 19.75m d) 20m

8. gbLsf] Ps lsgf/fdf 36 ld= cUnf] :tDe 5 . gbLsf] csf{] lsgf/faf6 :tDesf] 6K' kfd] ff x]bf{ pGgtf+z sf]0f 60o /x5] eg]

gbLsf] rf8} fO kQf nufpgx' f];\ .

a) 36/ 3 b) 36 3 c) 36/ 2 m d) 36 2
Answer sheet 3. a 4. a
5. a 6. 7. d 8. a
1. a 2. a

Time and Work

A. kT| oIf ljr/0f (Direct Variation)

lbOPsf bO' {j6f /flzx?dWo] olb klxnf] /fzL a9b\ f bf;] |f] klg a9\5 / klxnf] 36\bf bf;] |f] klg 36\g] cj:yf cfp5F eg] tL b'O{
/fzLx?sf] ;DaGwnfO{ Direct Variation elgG5 .

Expample 1

olb /fdn] @) j6f lstfa lsGbf ?= %)) lt5{ eg] p;n] $) j6f lstfasf] slt k;} f lt5{ <

Solution:

20 j6f lstfa = ?= 500

1 cf]6f lstfa = 500 = 25
20

40 cf6] f lstfa = 25 × 40 = 1000 k5{ –
-

csf{] tl/sf

Direct Variation dN" o

lstfa

20 500

40 x

20 500
or, 40 = x

or, 20x = 20000

20000
or, x = 20

or, x = 1000 k5{ .
B) ck|ToIf ljr/0f (Indirect Variation)

lbOPsf b'O{j6f /fzLdWo] olb klxnf] /fzL a9\bf bf];f| ] 36g\ ] / klxnf] 36b\ f bf];f| ] a9\g] cj:yf cfpF5 eg] tL b'O{ /fzLx?sf]
;DaGwnfO{ Indirect variation elgG5 .

Example 2

@) hgf dflg;n] sg' } sfd $) lbgdf ug{ ;S5g\ eg] $) hgf dflg;n] pQm sfd slt lbgdf ug{ ;S5g\ .

Solution:

20 hgf = 40 lbg
1 hgf = 40 × 20 = 800 lbg

40 hgf = 800 = 20 lbg
40

Indirect Variation

dflg; lbg

20 hgf 40 lbg

40 hgf x

x 20
or, 40 = 40

or, 40x = 800

800
or, x = 40

or, 20 lbg

Example 3

#) hgf dflg;n] s'g} sfd @) lbgdf ug{ ;S5g\ eg] !) lbgdf ;Sg slt dflg; yKg'knf{ <

Solution:

dflg; lbg

30 20

30 + x 10

-–

30+x 20
or, 30 = 10

or, 30 + 10x = 600
or, 10x = 600 – 300

300
or, x = 10

or, 30 hgf dflg; yKgk' nf{

Example 4

/fdn] sg' } sfd !% lbgdf / l;tfn] #) lbgdf ug{ ;S5g\ eg] bj' } hgfn] ldln ;f] sfd slt lbgdf ;S5g\ <

Solution:

/fdn] 1 sfd ug{ 1 lbg (15 lbgdf /fd 1)
15

l l;tfn] 1 sfd ug{ 1 lbg (1 lbgdf /fdn] 1 )
30 16

-/fd /+ l;tf_ n] 1 sfd ug{  1 + 1
15 30

2+1
= 30

3
= 30

1
= 10

/fd / l;tf ldn]/ pQm sfd ug{ 10 lbg nufp5F g\ .

Example 5

A eGg] wf/fn] 1 6o\ fs+ L kfgL 25 ldg]6df e5{ To:t} B eGg] wf/fn] ;f] 6\of+sL kfgL 20 ldg]6df vfnL u5{ eg] olb bj' }
wf/fx? Ps} ;fy vfN] g] xf] eg] Tof] 6o\ f+sL slt ;dodf el/Pnf <

Solution:

= 1 – 1
20 25

5–4
= 100

1
= 100

 pQm Ps 6\ofs+ L kfgL 100 ldg]6df el/G5 .

Exercise -1

1. 20 hgf dflg;n] sg' } sfd 15 lbgdf ug{ ;S5g\ eg] 10 lbgdf ;Sg slt dflg; yKg'knf{ <

(a) 5 hgf (b) 10 hgf (c) 15 hgf (d) 20 hgf

2. A n] sg' } sfd 10 lbgdf / B n] 15 lbgdf ug{ ;S5g\ eg] b'j} ldnL pQm sfd slt lbgdf ;S5g\ xfn] f <

-–

(a) 5 lbg (b) 6 lbg (c) 7 lbg (d) 8 lbg

3. 10 hgf dflg;n] sg' } sfd 7 lbgdf ;S5g\ eg] 14 hgf dflg;n] slt lbgdf ug{ ;S5g\ <

(a) 2 lbg (b) 3 lbg (c) 4 lbg (d) 5 lbg

4. /ljg ljsf;n] s'g} sfd 12 lbgdf ;S5g\ olb /ljgn] ;f] sfd 30 lbgdf ;S5 eg] ljsf; PSnn} ] slt lbgdf ;sfpF5
xfn] f <

(a) 30 (b) 20 (c) 15 (d) 10

5. 30 hgf dflg;n] 80 lbgdf ug{ ;Sg] sfd 20 lbgdf ug{ slt dflg; rflxG5 <

(a) 60 hgf (b) 100 hgf (c) 120 hgf (d) 80 hgf

6. Pp6f 3/ agfpg] sfd ug{ 3 hgf HofdLnfO{ 5 lbg nfU5 eg] 5 hgf HofdLn] ;f] sfo{ ug{ slt lbg nfU5 <

(a) 3 lbg (b) 5 lbg (c) 6 lbg (d) 8 lbg

7. Pipe's 'P and 'Q' can fill a tank is 5 and 6 hours respectively. Pipe 'R' can empty it in 12 hours. If all the
three pipes are opened together, then the tank will be filled in:

9 8 13 1
(a) 317hrs (b) 211hrs (c) 117 hrs (d) 42 hrs

8. Sonia takes 8 hrs to do a work. Gita takes 10 hrs to do the same work. How long should it take both
Sonia and Gita working together to do the same work?

40 4 2 (d) none of these
(a) 8 hrs (b) 49 hrs (c) 58 hrs

9. P and Q can do a piece of work in 18 days Q and R can do it in 24 days. P and R can do it in 36 days. In
how many days will P, Q and R finish it, working together?

(a) 15 days (b) 12 days (c) 17 days (d) 16 days

10. 600 l;kfxLsf] Ps 8km\kmfnfO{ 50 lbgsf] nflu vfgf k¥' ofOPsf] lyof] . olb 15 lbg kl5 180 l;kfxLn] ;f]
8km\kmfdf 5f8] /] uP5g\ eg] afsF L vfgf slt lbgnfO{ kU' nf <

a) 35 lbg b) 40 lbg c) 45 lbg d) 50 lbg

11. Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute.
At this rate, how many bottles could 10 such machines produce in 4 minute?

a) 648 b) 1800 c) 2700 d) 10800

12. A Fort has provided of food for 150 men for 45 days. After 10 days, 25 men left the fort the number of
days for which the remaining food will last is:

a) 29 1 1 c) 42 d) 54
5 b) 37

4

13. 39 hgf dflg;n] Pp6f /f]8 agfpg bl} gs 5 306f sf] b/n] sfd ubf{ 12 lbgdf ;S5g\ eg] ;f] sfd 30 hgf
dflg;n] bl} gs 6 306fsf] b/n] ubf{ slt lbgdf ;S5g\ .

a) 10 b) 13 c) 14 d) 15

14. In a camp, there is a meal for 120 men or 200 children. It 150 children have taken the meal how many
men will be catered to with remaining meal?

a) 20 b) 30 c) 40 d) 50

Profit and Loss

-–

Gfkmf gfS] ;fg ;DaGwL ;q' x?

!_ gfkmf Ö lj=d"= – qm=d" @_ ljqmL dN" o Ö qm=d"=± gfkmf

#_ gf]S;fg Ö qm=d=" – lj=d"= $_ qmo dN" o Ö lj=d" – gfkmf

%_ lj=d=" Ö qm=d"= – gfS] ;fg ^_ qmo dN" o Ö lj=d=" ± gfS] ;fg

& gfkmf Ü Ö jf:tljs gfkmf × !))Ü *_ gf]S;fg Ü Ö jf:tljs gf]S;fg × !))Ü
qm=d"= qm=d"=

(_ 56' Ü Ö 56' × !))Ü !)_ lj=d=" -56' / Eof6 lbPdf_ Ö c=d'= – 5'6 ± Eof6
c=d="

Exercise

!_ ?= !)) df lslgPsf] ;fdfgnfO{ @)Ü gfkmf ul/ aR] bf sltdf aR] g' knf{ <

s_ *) v_ !)) u_ !@) 3_ !@%

@_ s'g} ;fdfg ?= #@) df aR] bf @)Ü gfS] ;fg xG' 5 eg] @)Ü gfkmf ug]{ sltdf a]Rg' knf{ <

s_ $)) v_ $$) u_ $*) 3_ %))

#_ s[i0fn] Pp6f sf6] nfO{ $%) df a]Rbf !)Ü gf]S;fg eP5 eg] To;sf] qmod"No slt xfn] f <

s_ $%) v_ %)) u_ $)) 3_ %%)

$_ ljsf;n] Pp6f ;fOsn ?= @))) df lsg/] ?= @*)) df aR] bf slt gfkmf x'G5 .

s_ %)) v_ *)) u_ !))) 3_ !@))

%_ /ldnfn] Pp6f ;f8L ?= %)) df lsg]/ ?= $)) df aR] bf slt kl| tzt gfS] ;fg x'G5 <

s_ !) v_ @% u_ #) 3 @)

^_ ?= $)) kg]{ Pp6f /8] Lof] !)Ü 56' df lsg/] @)Ü gfkmf vfO{ a]Rbf sltdf a]Rg' knf{

s_ $!) v_ $@) u_ $#@ 3_ $%)

&_ k|ltuf6] f ?= !) kg]{ snd !)Ü 56' lbP/ @ bh{g aR] bf hDdf ljqmo dN' o slt xf]nf

s_ !)* v_ @)) u_ @!^ 3_ s'g} klg xf]Og

*_ Ps hgf ls;fgn] ?= *)) df lsg]/ v;L $ aif{ kl5 ^)Ü gfkmf vfP/ a]Rbf sltdf a]Rof] xfn] f <

s_ %)) v_ #&) u_ !@$) 3_ !@*)

(_ !%)) sf] ;fdfgdf %Ü 56' lbbf slt /sd ltg{' knf{ <

s_ !$%) v_ !$@% u_ !$)) 3_ !#%)

!)_ ?= ! sf] $ cf]6f ;'Gtnf lsg/] ?= ! sf] # cf6] fsf b/n] aR] bf slt k|ltzt gfkmf xG' 5 <

s_ @)Ü v_ #) u_ ##=## Ü 3_ #&=%#Ü

!!_ Pp6f ;fdfgsf] qmo dN' o lj=dN" o eGbf @)Ü tn 5 eg] gfkmf k|ltzt slt xfn] f <

s_ @)Ü v_ @%Ü u_ %)Ü 3_ #)Ü

!@_ Pp6f sk8f @)Ü 56' kl5 ? !))) df lslgof] olb !)Ü dfq 5'6 ePsf] eP To; ;fdfgx? slt ltg{k' g]{ lyof] <

s_ !@)) v_ !!%) u_ !!@% 3_ !!))

!#_ olb !)Ü 56' lbP/ !) Ü Eof6 nufpbf Pp6f j:t'sf] dN' o %)) eP5 eg] c+lst dN" o slt xf]nf <

s_ $%) v_ $(% u_ %)) 3_ %!)

!$_ s'g} ;fdfg @)Ü gfkmf ug{ @$) df ljqmL ug'{ k5{ eg] @%Ü gfkmf ug{ sltdf aR] g' knf{

-–

s_ @%) v_ @$% u_ @$) 3_ @&)
%= -3_ ^= -u_ &= -u_ *= -3_
Answer Sheet Profit and Loss

!= -u_ @= -u_ #= -v_ $= -v_ (= -v_ !)= -u_
!$=-s_
‼= -v_ !@= -u_ !#= -v_

h) Data Interpretation

1) Charts

l8u|LnfO{ ?= df kl/jt{g ubf{ hDdf x, ?= nfO{ l8uL| df kl/jt{g ubf{ 360°  x,

360°  hDdf

l8u|LnfO{ Ü df kl/jtg{ ubf{ 100  x, Ü nfO{ l8uL| df kl/jtg{ ubf{ 360°  x,
360° 100

Example:

Pp6f ;dfx/f]df pkl:yt ePsf ()) hgf ljBfyLx{ ?nfO{ eljiodf s] aGg] egL ;fl] wPsf] k|Zgdf plgx?af6 kf| Kt
kl| tlqmofnfO{ ;uF }sf] kfOrf6{df b]vfOPsf] 5 .

Pie chart 8fS6/

i) slt hgfn] …8fS6/Ú aGg] OR5f JoQm u/] . jlsn 90°

ii) slt hgfn] …kfOn6Ú aGg] OR5f JoQm u/] . 80° kfOn6
iiii) slt hgfn] …lzIfsÚ aGg] OR5f JoQm u/] . 50°

iv) slt hgfn] …jlsnÚ aGg] OR5f JoQm u/] . lzIfs

Solution:

i) 8fS6/ aGg rfxg] = 900  90 = 225 hgf ii) kfOn6 aGg rfxg] = 900  80 = 200 hgf
360 360

iii) lzIfs aGg rfxg] = 900  50 = 150 hgf iv) jlsn aGg rfxg] = 900  (360 – 220) = 350 hgf
360 360

2) Graphs

Histogram -:tDe lrq_
Example tn lbOPsf] :tDe lrq (Histogram) cWoog u/L lgDg kZ| gx?sf] pQ/ lbgx' f;] \ .

-–

10

9

8

7

6

5

4

3

2
1

0 4 8 12 16 20
d) 4
k|fKtfÍ d) 32
d) 12 – 16
i) !@ bl] v !^ c+s k|fKt ug{] ljBfyL{ ;V+ of slt xf]nfg\ < d) 20%

a) 10 b) 6 c) 8

Soln: c) 8 hgf

ii) hDdf ljBfyL{ ;+Vof slt xfn] f <

a) 30 b) 34 c) 28

Soln: c) 32 hgf

iii) a9L ljBfyL{ ;V+ of ePsf] k|fKtfÍ ;dx' sg' xf] <

a) (0 – 4) b) 4 – 8 c) 8 – 12

Soln: c) (8 – 12)

iv) -!@ – !^_ c+s k|fKt ug{] ljBfyLs{ f] k|ltzt slt xfn] f <

a) 40% b) 30% c) 25%

Soln: 8  100 = 25%
32

3) Tables -tflnsf_

tnsf] tflnsf cWoog u/L ;fl] wPsf kZ| gx?sf] ;xL pQ/ lbg'xf];\ .

jif{ 2012 2013 2014 2015 2016 2017 2018
246
:ofp pTkfbg kg df 180 200 240 210 229 195 250

;G' tnf pTkfbg kg df 185 190 170 200 215 240

i) @)!@ ;fnbl] v @)!* ;fn;Dd :ofp slt kg pTkfbg eP5 <

a) 1500 kg b) 1505 kg c) 1530 kg d) 1540 kg

Soln: (a) 1500 kg (180 + 200 + 240 + 210 + 229 + 195 + 246)

ii) @)!@ ;fnb]lv @)!* ;fn;Dd ;'Gtnf slt kg pTkfbg eP5 <

a) 1445 kg b) 1440 kg c) 1450 kg d) 1460 kg

Soln: (c) 1450 kg (185 + 190 + 170 + 200 + 215 + 240 + 250)

iii) @)!# ;fnsf] t'ngfdf @)!$ ;fndf :ofp pTkfbg slt kl| tztn] j[l4 ePsf] b]lvG5 <

a) 30% b) 20% c) 15% d) 12.5%

Soln: j[l4 Ü = 40  100 = 20%
200

-

iv) @)!@ ;fnb]lv @)!* ;fn;Ddsf] pTkfbg kl/0ffdsf] t'ngfdf :ofp / ;'Gtnf dWo sg' sd xfn] f <

a) :ofp b) ;G' tnf c) A / B b'j} a/fa/ d) None of these

Soln: (b) ;G' tnf

i) Find the Wrong Term in the Series

In each of the following questions, one term in the number series is wrong. Find out the wrong term.

Exercise-1

1. 196, 169, 144, 121, 101

(a) 101 (b) 121 (c) 169 (d) 196

2. 3, 10, 27, 4, 16, 64, 5, 25, 125

(a) 3 (b) 4 (c) 10 (d) 27

3. 2, 5, 10, 17, 26, 37, 50, 64

(a) 17 (b) 26 (c) 37 (d) 64

4. 2, 4, 8, 16, 32, 62

(a) 2 (b) 62 (c) 32 (d) 16

5. 10, 11, 9, 12, 8, 14

(a) 10 (b) 9 (c) 14 (d) 8

6. 2, 5, 10, 50, 500, 5000

(a) 5 (b) 50 (c) 500 (d) 5000

7. 2, 6, 12, 20, 28

(a) 28 (b) 20 (c) 12 (d) 2

8. 0, 2, 8, 12, 24, 35

(a) 0 (b) 12 (c) 24 (d) 35

9. 3, 7, 15, 31, 63, 128

(a) 7 (b) 31 (c) 128 (d) None of these

10. 2, 9, 28, 65, 125

(a) 125 (b) 28 (c) 9 (d) 2

Answer Sheet

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

g) Percentage, Fraction, Decimal, Average, Ratio

A) Percentage
k|To]s !)) df sg' } lglZrt efu tyf cz+ nfO{ k|ltzt elgG5 .

Some Important Formula

!_ gfkmf Ü Ö jf:tljs gfkmf × !))Ü @_ gfS] ;fg Ü Ö jf:tljs gfS] ;fg × !))Ü
qm=d"= qm=d"=

#_ al[ 4 Ü Ö j[l4 × !))Ü $_ 56' Ü Ö 5'6 × !))Ü
;?' sf] dN" o ;'?sf] dN" o

%_ kf| KtfÍ Ü Ö k|fKt u/s] f] c+s × !))Ü ^_ s/sf] Ü Ö lt/s] f] s/ × !))Ü
k"0ff+{s s/ofU] o cfDbfgL

pbfx/0f

!_ !%) hgfsf] !) kl| tzt slt xG' 5,

oxfF, ;q' cg';f/, 150 × 10 =5 hgf
100

@_ slt ;V+ ofsf] @) kl| tzt $) x'G5 <

cfjZos ;Vof Ö 40 × 100 = 200 xG' 5 .
20

#_ /fdsf] 3/ef8f ?= %))) af6 36/] ?= $))) eof] eg] lghsf] 3/ef8f slt kl| tztn] 36o\ f] .

5000 – 4000
= 5000 × 100

1000 × 100
= 5000

= 20%

Exercise 1 (Percentage) k|ltzt
!_ sltsf] @%Ü n] %)) xG' 5 <

s_ !%)) v_ @))) u_ @%)) 3_ #)))

@_ $%) sf] !)Ü slt xG' 5 <

s_ $) v_ $% u_ %) 3_ %%

#_ %)) sf] !%Ü eg]sf] slt xG' 5 <

s_ %% v_ ^% u_ &% 3_ *)

$_ !))) sf] #%Ü eg]sf] slt xG' 5 <

s_ #)) v_ #@) u_ #%) 3_ %))

%_ ?= @%) sf] slt k|ltzt &% x'G5 <

s_ #)Ü v_ #%Ü u_ $%Ü 3_ @%Ü

^_ Ps rfy} fO{ egs] f] slt xG' 5 <

s_ !%Ü v_ @)Ü u_ @%Ü 3_ %)Ü

&_ ?= !) nfO{ @)Ü n] a[l4 ubf{ slt xG' 5 <

s_ !@ v_ !% u_ !^ 3_ !*

*_ nf]s;]jf cfofu] sf] kl/Iff b:t'/ ?= %)) af6 al[ 4 eP/ ?= ^)) k'Uof] eg] slt k|ltzt n] al[ 4 eof] xfn] f <

s_ @%Ü v_ @)Ü u_ #%Ü 3_ !)Ü

(_ ?= !)) df lslgPsf] ;fdfgnfO{ @%Ü gfkmf ul/ j]Rbf sltdf a]Rg' knf{ <

s_ &% v_ !)) u_ !@% 3_ !%)

!)_ ?= @$) df a}Rbf @%Ü gfS] ;fg xG" 5 eg] @%Ü gfkmf vfP/ aR] bf sltdf aR] g' knf{ <

s_ $)) v_ #^) u_ #*) 3_ $@)

!!_ Pp6f k;n]n] u'nfkmsf] yª' \uffnfO{ To;sf] dN' odf @)Ü 36fP/ aR] bf ?= $)) x'G5 eg] ;f] kmn' sf] 36fpg'
cuf8Lsf] d'Vo slt xfn] f <

s_ ?= *)) v_ ?= &)) u_ ?= &)) 3_ ?= %))

!@_ lq=lj=sf] k/LIffdf !)) hgf s]6fx?n] k/LIff lbPsfd] f @) hgf dfq plt0f{ eP5g\ eg] slt kl| tzt s]6fx?
cgl' t0f{ eP5g\ <

s_ $)Ü v_ ^)Ü u_ *)Ü 3_ ()Ü

!#_ @) sf] @%Ü / #) sf] !)Ü sf] km/s slt xG' 5 <

s_ ! v_ @ u_ # 3_ $

!$_ Pp6f sIffsf7] fdf ePsf ljBfyLs{ f] $)Ü s]6L lyP / afsL ^) hgf s6] fx? lrP eg] hDdf ljBfyL{ slt lyP
xf]nfg\ .

s_ !)) hgf v_ !$) hgf u_ @)) hgf 3_ @$) hgf

!%_ /fdn] %)) j6f cfn' ePsf] Ps af]/f cfn' lsg5] h;df @% a6f cfn' ljluP| sf] kfOof] eg] slt k|ltzt /fd|f cfn'
5g\ xf]nf <

s_ @%Ü v_ !%Ü u_ *%Ü 3_ (%Ü

!^_ ljsf;n] IQ df $)Ü / lg;fn] ^)Ü c+s kfP5g\ . olb pgLx?sf] kf| KtfÍsf] cGt/ @) eP IQ ljifosf] k"0ff{Í
slt xf]nf <

s_ %) v_ *) u_ !)) 3_ @$)

!&_ olb sg' } /sdsf] @%Ü a/fj/ %)) x'G5 eg] pQm /sdsf] @÷$ efu slt x'G5 <

s_ !))) v_ !%)) u_ @))) 3_ @%))

!*_ Pp6f TV sf] dN' odf @)Ü 5'6 lbbf /fdn] Pp6f TV lsGbf ?= !@)) ltgk'{ Yof] eg] TV sf] 5'6 glbbfsf] dN' o
slt /x5] <

s_ !$))) v_ !%)) u_ !*)) 3_ @)))

!(_ ;fgn' ] cfkm\gf] bl} gs ks6] vr{ ?= %)) dWo] ?= !%) vr{ u/L eg] p;n] slt kl| tzt vr{ u/L <

s_ @)Ü v_ @%Ü u_ #)Ü 3_ $%Ü

@)_ !$) sf] slt k|ltzt %)) sf] &Ü ;Fu a/fj/ xf]nf <

s_ @%Ü v_ #%Ü u_ $@Ü 3_ %)Ü

@!_ * nfO{ !) jgfpbF f slt k|ltzt a[l4 xG' 5 <

s_ !%Ü v_ @)Ü u_ @%Ü 3_ #)Ü

Answer Sheet Percentage Exercise 1

!= -v_ @= -v_ #= -u_ $= -u_ %= -s_ ^= -u_ &= -s_

*= -v_ (= -u_ !)= -s_ !!= -3_ !@= -u_ !#= -v_ !$= -s_

!%= -3_ !^= -u_ !&= -s_ !*= -v_ !(= -u_ @)= -s_ @!= -u_

Fraction -leGg_

!_ leGgnfO{ bzdnjdf nfFbfx?n] cz+ nfO{ efu ugk'{ 5{ <

sf]lzz zl} Ifs sG] b| -nfs] ;j] f –

h:t} M ! Ö )=%,
@

@ Ö )=%
$

@_ leGgnfO{ k|ltztdf nfbF f !)) n] u'0ffg ul/ k|ltzt lrGx| /fVg' k5{ <

!
@

! × !)) Ö %)Ü
@

@ × !)) Ö $)Ü
%

cs+ j/fj/ h:tf] ePdf ;fgf] cªs\ eP ;fgf] / 7n" f] cs+ ePdf 7n" f] x'G5 <

Exercise 2

!_ tn lbOPsf] leGgx? (Fraction) dWo] ;ae} Gbf 7n" f] leGg sg' xf] <

s_ $÷% v_ %÷& u_ !)÷!! 3__ !@÷!#

@_ tn lbOPsf] (Fraction) dWo] ;j}eGbf ;fgf] leGg sg' xf] <

s_ $÷% v_ %÷& u_ !)÷!! 3_ !@÷!#

#_ tn lbOPsf leGgx? (Fraction) dWo] ;j} eGbf 7n" f] leGg sg' xf] <

s_ $)÷& v_ #%÷$ u_ %$÷* 3_ &@÷&

$_ tn lbOPsf leGgx? (Fraction) dWo] ;j} eGbf ;fgf] leGg sg' xf] <

s_ #%÷& v_ #%÷$ u_ #$÷* 3_ &@÷&

%_ @÷!) nfO{ bzdnjdf nh} fbF f slt xG' 5 <

s_ )=))@ v_ )=)@ u_ )=@ 3_ @

^_ $÷!)) nfO{ bzdnjdf n}hfbf slt x'G5 <

s_ $ v_ )=)$ u_ )=))$ 3_ )=$

&_ %÷!))) nfO{ bzdnjdf n}hfb slt xG' 5 <

s_ )=)% v_ )=))% u_ % 3_ %=))

*_ #÷( nfO{ bzdnjdf nh} fbf slt xG' 5 <

s_ # v_ )=!# u_ )=## 3_ )=$

(_ $÷@% nfO{ bzdnjdf nh} fbf slt xG' 5 <

s_ !=^ v_ )=!^ u_ )=)!^ 3_ @

!)_ @÷% nfO{ k|ltztdf nh} fbf slt x'G5 <

s_ @)Ü v_ $)Ü u_ &)Ü 3_ #)Ü

!!_ #÷$ nfO{ kl| tztdf nh} fbf slt xG' 5 <

s_ @%Ü v_ %)Ü u_ &%Ü 3_ ()Ü

!@_ !÷@) nfO{ kl| tztdf nh} fbf slt xG' 5 <

s_ $Ü v_ %Ü u_ &Ü 3_ !)Ü
-

!#_ ^÷@% nfO{ kl| tztdf n}hfbf slt xG' 5 <

s_ !%Ü v_ @)Ü u_ @$Ü 3_ @%Ü
3_ #÷@)
!$_ !%Ü nfO{ leGgdf n}hfbf slt x'G5 < 3_ @÷@%
3_ @÷@%
s_ @÷!) v_ #÷!) u_$÷!) &= -v_ *= -u_

!%_ !^Ü nfO{ leGgdf n}hfbf slt x'G5 <

s_ @÷@) v_$÷@) u_ $÷@%

!^_ #%Ü nfO{ leGgdf n}hfbf slt x'G5 <

s_ &÷@) v_ ^÷@% u_ ^÷@)

Answer Sheet Fraction (= -v_ !)=-v_

!= -3_ @= -s_ #= -3_ $= -u_ %= -u_ ^= -v_

!!= -u_ !@= -v_ !#= -u_ !$= -3_ !%= -u_ !^= -s_

Decimal -bzdnj_

bzdnjnfO{ leGgdf nfbF f bzdnj lrGx| x6fpg' k5{ .

!_ h:t} 0.4 = 04 = 2 = 0.25 = 100 = 1
10 5 025 4

bzdnjnfO{ kl| tztdf nfbF f !)) n] u0' ffg ul/ Ü lrGx /fVg' k5{ .

!_ )=#

)=# × !))Ü

# × !)

#)Ü

@_ )=@%

)=@% × !))Ü

@% × !

@%Ü cflb .

k|ltztnfO{ bzdnjdf nUbf leGgdf nuL x/n] c+znfO{ efu ug'{ k5{ .

h:t} @)Ü nfO{ bzdnjdf nUbf,

20
100 = 0.2

!_ )=@% nfO{ leGgdf nh} fbf slt xG' 5 <

s_ !÷@ v_ !÷$ u_ !÷* 3_ !÷%

@_ )=@ nfO{ leGgdf nh} fbf slt x'G5 <

s_ !÷% v_ !÷@ u_ !÷$ 3_ !÷^

#_ )=!% nfO{ leGgdf n}hfbf slt x'G5 <

s_ @÷!@ v_ #÷!& u_ #÷@) 3_ #÷%

$_ )=!@% nfO{ leGgdf nh} fbf slt xG' 5 <

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