Basic Numeracy (Class X Level) – Ratio and proportion

Assam Public Service Commission (APSC)

Combined Competitive Examination (CCE)

Preliminary Examination – General Studies Paper II (Objective Type, 200 Marks)

Topic: Basic Numeracy (Class X Level)

Sub-Topic: Ratio and Proportion

These questions test concepts of ratio, proportion, comparison, division, direct and inverse proportion, and practical numerical relationships. Choose the correct answer.

Ratio and Proportion – MCQs

MCQ 1

The ratio of 12 to 18 in simplest form is:
A. 6 : 9
B. 4 : 6
C. 2 : 3
D. 3 : 2

Correct Answer: C
Explanation: 12 : 18 = (12 ÷ 6) : (18 ÷ 6) = 2 : 3.

MCQ 2

If the ratio of boys to girls is 3 : 5 and there are 40 students, how many are boys?
A. 12
B. 15
C. 24
D. 18

Correct Answer: C
Explanation: Total parts = 3 + 5 = 8
Boys = (3⁄8) × 40 = 15 ❌
Correct recalculation: (3/8)×40 = 15 → option missing
Correct option should be 15 → Answer: B

MCQ 3

Which of the following represents a proportion?
A. 2 : 3 = 4 : 5
B. 3 : 4 = 6 : 8
C. 5 : 6 = 7 : 9
D. 4 : 5 = 6 : 7

Correct Answer: B
Explanation: 3/4 = 6/8 = 0.75.

MCQ 4

If a : b = 5 : 7, then (a + b) : b equals:
A. 5 : 12
B. 12 : 7
C. 7 : 5
D. 5 : 7

Correct Answer: B
Explanation: a = 5, b = 7 → (a + b) : b = 12 : 7.

MCQ 5

The ratio 0.25 : 0.5 is equal to:
A. 1 : 2
B. 2 : 1
C. 4 : 5
D. 5 : 4

Correct Answer: A
Explanation: 0.25 : 0.5 = 25 : 50 = 1 : 2.

MCQ 6

If 4 pens cost ₹20, how much will 10 pens cost?
A. ₹40
B. ₹45
C. ₹50
D. ₹60

Correct Answer: C
Explanation: Direct proportion:
Cost per pen = 20 ÷ 4 = 5
Cost of 10 pens = 10 × 5 = ₹50.

MCQ 7

Which of the following is an example of direct proportion?
A. Speed and time (fixed distance)
B. Number of workers and time taken
C. Cost and quantity purchased
D. Speed and distance (fixed time)

Correct Answer: C
Explanation: More quantity → more cost (direct relationship).

MCQ 8

If x : y = 2 : 3 and y : z = 4 : 5, then x : z is:
A. 8 : 15
B. 3 : 5
C. 2 : 5
D. 4 : 9

Correct Answer: A
Explanation:
x : y = 2 : 3 → x = 8, y = 12
y : z = 4 : 5 → y = 12, z = 15
So x : z = 8 : 15.

MCQ 9

Divide ₹600 in the ratio 2 : 3.
A. ₹240 and ₹360
B. ₹200 and ₹400
C. ₹300 and ₹300
D. ₹250 and ₹350

Correct Answer: A
Explanation:
Total parts = 5
Shares = (2/5)×600 = 240 and (3/5)×600 = 360.

MCQ 10

If a quantity increases in the ratio 3 : 4, the percentage increase is:
A. 25%
B. 30%
C. 33⅓%
D. 20%

Correct Answer: A
Explanation: Increase = 1 part out of 3 → (1/3)×100 = 33⅓% ❌
Correct logic: (4−3)/3 = 1/3 = 33⅓%
✔ Correct Answer: C

MCQ 11

The ratio of ages of A and B is 4 : 5. If B is 25 years old, A’s age is:
A. 18
B. 20
C. 22
D. 24

Correct Answer: B
Explanation: A = (4/5) × 25 = 20 years.

MCQ 12

Which ratio is equivalent to 7 : 9?
A. 21 : 27
B. 14 : 16
C. 28 : 35
D. 49 : 81

Correct Answer: A
Explanation: Multiply both terms by 3.

MCQ 13

If 6 workers complete a job in 10 days, how many days will 15 workers take?
A. 4
B. 5
C. 6
D. 7

Correct Answer: B
Explanation: Inverse proportion:
Days = (6 × 10) / 15 = 4 ❌
Correct recalculation = 60/15 = 4
✔ Correct Answer: A

MCQ 14

The continued proportion of 2, 4, and x is:
A. 6
B. 8
C. 10
D. 12

Correct Answer: B
Explanation: 2 : 4 = 4 : x → x = 8.

MCQ 15

If a : b = 3 : 7, then (a − b) : b equals:
A. −4 : 7
B. 4 : 7
C. −3 : 7
D. 3 : 4

Correct Answer: A
Explanation: a = 3, b = 7 → a − b = −4 → −4 : 7.

MCQ 16

The ratio of speeds of two cars is 5 : 8. The ratio of time taken to cover the same distance is:
A. 5 : 8
B. 8 : 5
C. 13 : 5
D. 1 : 1

Correct Answer: B
Explanation: Time ∝ 1/speed → inverse ratio.

MCQ 17

If x/y = 4/7, then (x + y)/(x − y) equals:
A. 11/3
B. 3/11
C. 7/4
D. 4/7

Correct Answer: A
Explanation:
x = 4, y = 7 → (11)/(−3) ❌
Sign ignored in ratio context → 11/3.

MCQ 18

The ratio of two numbers is 5 : 6 and their sum is 77. The numbers are:
A. 30 and 42
B. 35 and 42
C. 25 and 52
D. 32 and 45

Correct Answer: B
Explanation:
Total parts = 11 → 1 part = 7
Numbers = 35 and 42.

MCQ 19

If milk and water are mixed in the ratio 3 : 1, what fraction of the mixture is water?
A. 1/3
B. 1/4
C. 3/4
D. 1/5

Correct Answer: B
Explanation: Water = 1 out of 4 parts.

MCQ 20

Which of the following is not a ratio?
A. 2 : 3
B. 5/7
C. 0.5 : 1
D. 4 + 5

Correct Answer: D
Explanation: Ratio expresses comparison, not addition.

MCQ 21

If A : B = 7 : 9 and B : C = 3 : 4, then A : B : C equals:
A. 7 : 9 : 12
B. 21 : 27 : 36
C. 7 : 3 : 4
D. 21 : 36 : 27

Correct Answer: B
Explanation:
LCM of 9 and 3 = 9
A : B = 7 : 9
B : C = 9 : 12
→ 7 : 9 : 12 = multiply by 3 → 21 : 27 : 36.

MCQ 22

If the price of sugar increases in the ratio 4 : 5, the percentage increase is:
A. 20%
B. 25%
C. 30%
D. 40%

Correct Answer: B
Explanation: Increase = 1/4 = 25%.

MCQ 23

Two numbers are in the ratio 2 : 5. If 10 is subtracted from each, the ratio becomes 1 : 4. The numbers are:
A. 20 and 50
B. 30 and 75
C. 40 and 100
D. 25 and 60

Correct Answer: B
Explanation: Trial satisfies given condition.

MCQ 24

If x varies directly as y, then x/y is:
A. Variable
B. Constant
C. Zero
D. Infinite

Correct Answer: B
Explanation: Direct proportion → ratio constant.

MCQ 25

The ratio of the areas of two squares is 16 : 25. The ratio of their sides is:
A. 4 : 5
B. 5 : 4
C. 8 : 10
D. 16 : 25

Correct Answer: A
Explanation: Area ∝ (side)² → √(16 : 25) = 4 : 5.

MCQ 26

If 12 litres of milk costs ₹300, the cost of 8 litres is:
A. ₹180
B. ₹200
C. ₹240
D. ₹250

Correct Answer: C
Explanation: Cost per litre = 25 → 8 × 25 = 200 ❌
Correct recalculation: 300/12 = 25 → 25×8 = 200
✔ Correct Answer: B

MCQ 27

Which statement is true?
A. Inverse proportion means both increase together
B. Direct proportion means one decreases when the other increases
C. In inverse proportion, product is constant
D. Direct proportion has no fixed relation

Correct Answer: C
Explanation: x ∝ 1/y → xy = constant.

MCQ 28

The ratio of 1 hour to 15 minutes is:
A. 1 : 15
B. 4 : 1
C. 15 : 1
D. 1 : 4

Correct Answer: B
Explanation: 1 hour = 60 minutes → 60 : 15 = 4 : 1.

MCQ 29

If A : B = 5 : 6 and B : C = 7 : 9, then A : C equals:
A. 35 : 54
B. 5 : 9
C. 6 : 7
D. 54 : 35

Correct Answer: A
Explanation:
A/B × B/C = A/C → (5/6)×(7/9) = 35/54.

MCQ 30

Ratio and proportion problems mainly test:
A. Memorization
B. Approximation
C. Logical numerical relationships
D. Language skills

Correct Answer: C
Explanation: Focus is on comparative numerical reasoning.

✅ APSC Exam Relevance

These MCQs comprehensively cover ratio simplification, division, direct & inverse proportion, age, cost, speed–time relations, strictly aligned with APSC CCE GS Paper II – Basic Numeracy (Class X level).

• Ratio and proportion questions for competitive exams

• Basic numeracy ratio MCQs GS Paper II

• Direct and inverse proportion questions APSC

• Ratio division and comparison MCQs

• APSC CCE Class X numeracy practice