SSC CGL Preparation – Day 14

MCQ – Ratio and Proportion

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1. The ratio of two numbers is 3:4. If their sum is 112, find the numbers.
A. 48 and 64
B. 42 and 70
C. 60 and 52
D. 50 and 62

👉 Solution:
Let the numbers be 3x and 4x
3x + 4x = 112 ⇒ 7x = 112 ⇒ x = 16
⇒ Numbers = 3×16 = 48 and 4×16 = 64
✅ Answer: A

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2. A sum of ₹1,440 is divided between A and B in the ratio 5:7. What is A’s share?
A. ₹600
B. ₹700
C. ₹800
D. ₹640

👉 Solution:
Total parts = 5 + 7 = 12
A’s share = (5/12) × 1440 = ₹600
✅ Answer: A

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3. The ratio of the ages of A and B is 4:5. After 5 years, the ratio becomes 5:6. Find A’s present age.
A. 20
B. 25
C. 30
D. 35

👉 Solution:
Let present ages be 4x and 5x
(4x + 5)/(5x + 5) = 5/6
⇒ 6(4x + 5) = 5(5x + 5)
⇒ 24x + 30 = 25x + 25
⇒ x = 5
⇒ A = 4x = 20
✅ Answer: A

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4. If A : B = 3 : 4 and B : C = 2 : 5, then A : B : C = ?
A. 3 : 4 : 10
B. 3 : 4 : 5
C. 6 : 8 : 20
D. 5 : 10 : 4

👉 Solution:
A : B = 3 : 4
B : C = 2 : 5 ⇒ Make B same:
A : B = 3×2 : 4×2 = 6 : 8
B : C = 2×4 : 5×4 = 8 : 20
⇒ A : B : C = 6 : 8 : 20
✅ Answer: C

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5. In what ratio should 30 litres of a solution with 40% alcohol be mixed with another solution with 60% alcohol to get a 50% alcohol solution?
A. 1:1
B. 2:1
C. 1:2
D. 3:1

👉 Solution (Alligation Rule):
Higher % = 60
Mean = 50
Lower % = 40
⇒ (60 − 50):(50 − 40) = 10:10 = 1:1
✅ Answer: A

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6. A and B together have ₹3,900. If 4/13 of A’s money equals 2/5 of B’s money, find A’s share.
A. ₹1,800
B. ₹2,000
C. ₹2,100
D. ₹2,300

👉 Solution:
Let A = a, B = b
Given: (4/13)a = (2/5)b
Cross-multiplying: 20a = 26b ⇒ a/b = 26/20 = 13/10
⇒ A:B = 13:10
⇒ Total parts = 13 + 10 = 23
A’s share = (13/23) × 3900 = ₹2,200
✅ Answer: Not in options (There may be a typo in options; correct A = ₹2,200)

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7. A sum of ₹1,200 is divided among A, B, and C in the ratio 2:3:5. What is C’s share?
A. ₹600
B. ₹500
C. ₹400
D. ₹300

👉 Solution:
Total parts = 2 + 3 + 5 = 10
C’s share = (5/10) × 1200 = ₹600
✅ Answer: A

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8. If x : y = 3 : 4 and y : z = 5 : 6, then x : y : z = ?
A. 15 : 20 : 24
B. 3 : 4 : 6
C. 12 : 16 : 20
D. 10 : 15 : 18

👉 Solution:
x : y = 3 : 4
y : z = 5 : 6
⇒ Make y same:
x : y = 3×5 : 4×5 = 15 : 20
y : z = 5×4 : 6×4 = 20 : 24
⇒ x : y : z = 15 : 20 : 24
✅ Answer: A

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9. Two numbers are in the ratio 5:7. If the smaller number is 75, what is the larger number?
A. 105
B. 90
C. 100
D. 95

👉 Solution:
Let numbers = 5x and 7x
5x = 75 ⇒ x = 15
Larger = 7x = 105
✅ Answer: A

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10. The ratio of income to expenditure of a person is 5:3. If he saves ₹1,200 per month, what is his income?
A. ₹3,000
B. ₹4,000
C. ₹5,000
D. ₹6,000

👉 Solution:
Let income = 5x, expenditure = 3x
Saving = Income − Expenditure = 2x = 1200 ⇒ x = 600
Income = 5x = ₹3,000
✅ Answer: A