Home Work-1

Q1. Two numbers are in the ratio 5 : 6. If 5 is subtracted from each

number, the ratio becomes 4 : 5. The numbers are:
a) 15, 20
b) 5, 10
c) 10, 15
d) 25, 30

Q2. Two numbers are in the ratio 3 : 4. If 6 is added to each term, the
new ratio becomes 4 : 5. The numbers are:
a) 24, 32
b) 18, 24
c) 15, 20
d) 9, 12

Q3. The angles of a triangle are in the ratio 2 : 7 : 11. The angles (in
degrees) are:
a) 20, 70, 110
b) 20, 70, 90
c) 30, 70, 80
d) 18, 63, 99

Q4. The daily earnings of Raj and Amit are in the ratio 4 : 5, and their
daily expenses are in the ratio 7 : 9. If each saves 50 per day, their
daily incomes () are:
a) (40, 50)
b) (50, 40)
c) (400, 500)
d) None of these

Q5. The sum of the ages of Ramesh, Suresh, and Dinesh is 150 years. Ten
years ago, their ages were in the ratio 7 : 8 : 9. Their present ages are:
a) 40, 60, 50
b) 50, 45, 55
c) 55, 35, 60
d) 45, 50, 55

Q6. Raj earns 80 in 7 hours, and Amit earns 90 in 12 hours. The ratio of
their earnings per hour is:
a) 32 : 21

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 b) 23 : 12
c) 8 : 9
d) None of the above
Q7. The ratio between the speeds of two trains is 7 : 8. If the second train
runs 400 km in 5 hours, the speed of the first train is:
a) 10 km/h
b) 70 km/h
c) 50 km/h
d) None of the above
Q8. The ratio of the speeds of two trains is 2 : 5. If the distances they
travel are in the ratio 5 : 9, the ratio of the times taken is:
a) 18 : 25
b) 5 : 4
c) 25 : 18
d) 1 : 1
a b c a+b+c
Q9. If = = , the value of is:
3 4 7 c
a) 1
b) 2
c) 3
d) None of the above
x y z 2x − 5y + 4z
Q10. If = = , the value of is:
2 3 7 2y
6
a)
23
17
b)
6
3
c)
2
d) None of the above
Q11. The ratio of 50 paise, Re. 1, and 5 coins with Amit is 5 : 2 : 1. If
the total amount is 38, the number of Re. 1 coins is:
a) 4
b) 8
c) 12
d) 16
Q12. Arun has coins of 5, 2, and 1 in the ratio 3 : 4 : 5. If the total amount
is 224, the number of 1 coins is:

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 a) 40
b) 35
c) 20
d) 30

Q13. Raj, Amit, and Vijay share an expense. Raj contributes 5 wood logs,
Amit contributes 4 wood logs, and Vijay contributes 9. Each wood log
is valued at 1, and the total value is divided equally among them. The
money Raj should receive to balance the contributions is:
a) 5
b) 4
c) 6
d) 3
√
r r
a b
Q14. If (a + b) : ab = 4 : 1, the value of + is:
b a
a) 1
b) 4
c) 2
d) 3
a b c
Q15. If = = , the value of each ratio is:
b+c c+a a+b
a) 1
1
b)
2
1
c)
20
d) None of the above

Q16. A stone worth 15,600 breaks into three pieces with weights propor-
tional to 2 : 3 : 5. The value varies as the cube of its weight. The
percentage loss is:
a) 80%
b) 90%
c) 84%
d) 78%

Q17. An employer reduces employees in the ratio 19 : 16 and increases

wages in the ratio 4 : 5. The ratio of initial to final wage bill is:
a) 20 : 19
b) 17 : 16

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 c) 16 : 17
d) 19 : 20

Q18. The
√ duplicate ratio of 3 : 4 is:
a) 3 : 2
b) 4 : 3
c) 9 : 16
d) None of these

Q19. The sub-duplicate ratio of 25 : 36 is:

a) 6 : 5
b) 36 : 25
c) 50 : 72
d) 5 : 6

Q20. The triplicate ratio of 2 : 3 is:

a) 8 : 27
b) 6 : 9
c) 3 : 2
d) None of these

Q21. The sub-triplicate ratio of 8 : 27 is:

a) 27 : 8
b) 24 : 81
c) 2 : 3
d) None of these

Q22. If p : q is the sub-duplicate ratio of (p − x2 ) : (q − x2 ), the value of x2

is:
p
a)
p+q
q
b)
p+q
c) 0
pq
d)
p−q
Q23. If 2s : 3t is the duplicate ratio of (2s − p) : (3t − p), then:
a) p = 6st
b) p2 = 6st
c) 2p = 3st
d) None of the above

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Q24. The compounded ratio of 2 : 3, 9 : 4, 5 : 6, and 8 : 10 is:
a) 1 : 1
b) 1 : 5
c) 3 : 8
d) None of these

Q25. The compounded ratio of 4 : 9 and the duplicate ratio of 3 : 4 is:

a) 1 : 4
b) 1 : 3
c) 3 : 1
d) None of these

Q26. The compounded ratio of 4 : 9, the duplicate ratio of 3 : 4, the

triplicate ratio of 2 : 3, and 9 : 7 is:
a) 2 : 7
b) 7 : 2
c) 2 : 21
d) None of these

Q27. The compounded ratio of the duplicate ratio of 4 : 5, the triplicate

ratio of 1 : 2, the sub-duplicate ratio of 81 : 256, and the sub-triplicate
ratio of 125 : 512 is:
a) 4 : 512
b) 3 : 32
c) 9 : 320
d) 1 : 120

Q28. The compounded ratio of 275 : 31, the inverse of 729 : 1331, the
duplicate ratio of 2 : 5, the triplicate ratio of 9 : 11, the sub-duplicate
ratio of 961 : 1296, and the sub-triplicate ratio of 729 : 1331 is:
a) 1 : 1
b) 1 : 2
c) 275 : 11
d) 31 : 25

Q29. The inverse ratio of 11 : 15 is:

a) 15
√ : 11√
b) 11 : 15
c) 121 : 255
d) None of these

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Q30. The ratio of two quantities is 5 : 7. If the consequent of its inverse
ratio is 5, the antecedent is:
a) 5√
b) 5
c) 7
d) None of these

Q31. Divide 5130 among P, Q, R, and S such that 3P = 4Q = 5R = 6S.

The share of Q is:
a) 1350
b) 1250
c) 1200
d) 1450
a 2 b 4
Q32. If = and = , the ratio a : b : c is:
b 3 c 5
a) 4 : 6 : 15
b) 4 : 8 : 15
c) 8 : 12 : 15
d) 8 : 16 : 25

Q33. If A : B = 2 : 3, B : C = 4 : 5, and C : D = 3 : 7, then A : B : C : D

is:
a) 4 : 6 : 15 : 35
b) 4 : 12 : 15 : 35
c) 8 : 12 : 15 : 35
d) 8 : 16 : 25 : 35

Q34. If a : b = 3 : 5, b : c = 5 : 4, c : d = 2 : 3, and d is 50% more than e,

the ratio a : e is:
a) 2 : 3
b) 3 : 4
c) 3 : 5
d) 4 : 5

Q35. Arun, Bharat, and Chirag work in a company. The ratio of Arun’s
age to Bharat’s age is 11 : 13, and Bharat’s age to Chirag’s age is 13 :
14. If the sum of their ages is 76, their ages are:
a) 33, 39, 42
b) 23, 27, 32
c) 22, 26, 28
d) 24, 28, 30

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Q36. Ravi and Sanjay have books in the ratio 3 : 4, while Sanjay and
Chetan have books in the ratio 3 : 2. If the total books are 116, the
number of books Ravi has is:
a) 36
b) 37
c) 32
d) 24
a 2 b 4 a+b
Q37. If = and = , the value of is:
b 3 c 5 b+c
a) 8 : 15
b) 20 : 27
c) 3 : 4
d) 27 : 20

Q38. The ratio of average temperatures between New Delhi and Hyderabad
is 11 : 12, and between New Delhi and Warangal is 9 : 8. The ratio of
average temperatures between Hyderabad and Warangal is:
a) 22 : 27
b) 27 : 22
c) 32 : 33
d) None of these

Q39. Ramesh distributes his property of 6,00,000 among his three sons.
The first son’s share is thrice the second’s, and the second’s share is
twice the third’s. The ratio of their shares is:
a) 1 : 2 : 6
b) 3 : 4 : 5
c) 6 : 2 : 1
d) 2 : 4 : 6

Q40. The fourth proportional to 4, 6, 8 is:

a) 12
b) 32
c) 48
d) None of these

Q41. The third proportional to 12, 18 is:

a) 24
b) 27
c) 36
d) None of these

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Q42. The mean proportional between 25 and 81 is:
a) 40
b) 50
c) 45
d) None of these

Q43. The number with the same ratio to 26 as 6 to 13 is:

a) 11
b) 12
c) 21
d) 10

Q44. The fourth proportional to 2a, a2 , and c is:

ac
a)
2
b) ac
2
c)
ac
d) None of these
1/2 1/5
Q45. If = , then x is:
1/3 1/x
6
a)
5
5
b)
6
15
c)
2
d) None of these

Q46. The mean proportional between 12x2 and 27y 2 is:

a) 18xy
b) 81xy
c) 8xy
d) None of these
x z y w
Q47. If = implies = , the process is called:
y w x z
a) Dividendo
b) Componendo
c) Invertendo
d) Alternendo
p r p−r
Q48. If = = , the process is called:
q s q−s

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 a) Subtrahendo
b) Addendo
c) Invertendo
d) None of these
a c a+b c+d
Q49. If = , then = is called:
b d a−b c−d
a) Componendo
b) Dividendo
c) Componendo & Dividendo
d) None of these
u w u−v w−p
Q50. If = , then = is called:
v p u+v w+p
a) Invertendo
b) Alternendo
c) Dividendo
d) Addendo
a b
Q51. If = , then:
4 5
a+4 b−5
a) =
a−4 b+5
a+4 b+5
b) =
a−4 b−5
a−4 b+5
c) =
a+4 b−5
d) None of these

Q52. What should be added to 3, 12, 48, 192 to make them proportional?
a) 3
b) 5
c) 7
d) 2

Q53. Four integers P, Q, R, S are in continued proportion. If P : R = 9 :

P
4, then is:
S
9
a)
4
27
b)
4 3/2
9
c)
4

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 d) 81

Q54. In what proportion must rice at 3.10/kg be mixed with rice at 3.60/kg
to get a mixture worth 3.25/kg?
a) 3 : 5
b) 5 : 3
c) 3 : 7
d) 7 : 3

Q55. Two groups of students have average scores of 30 and 40. The com-
bined average is 34. The ratio of the number of students in the groups
is:
a) 2 : 3
b) 3 : 5
c) 5 : 3
d) 3 : 2

Q56. A merchant has 100 kg of sugar. He sells part at 7% profit and the
rest at 17% profit, gaining 10% overall. The quantity sold at 7% profit
is:
a) 30 kg
b) 70 kg
c) 55 kg
d) 45 kg

Q57. Two solutions of 90% and 97% purity are mixed to get 21 litres of
95% purity. The quantity of 97% purity is:
a) 13 litres
b) 14 litres
c) 14.5 litres
d) 15 litres

Q58. 6.25 is made up of 80 coins of 10p or 5p. The number of each coin is:
a) 60, 20
b) 50, 30
c) 45, 35
d) 40, 40

Q59. A 300 gm sugar solution has 40% sugar. The sugar to be added to
make it 50% is:
a) 50 gm
b) 60 gm

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 c) 70 gm
d) 100 gm

Q60. An alloy of copper and zinc is in the ratio 9 : 4. The zinc required to
mix with 24 kg of copper is:
2
a) 10 kg
3
1
b) 10 kg
3
2
c) 9 kg
3
d) 9 kg

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