Ratio and Proportion — 24 Aptitude Questions and Answers with Explanations

Ratio and Proportion — Questions and Answers

Ratio and Proportion underlies partnership, mixtures, ages and data interpretation. The technique that saves the most time is the "k-method": write a : b = 3 : 4 as 3k and 4k, then let the condition in the question fix k. For chained ratios, make the common term equal by scaling rather than by converting to decimals.

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Ratio and Proportion— Concepts, Formulas & Shortcuts

a : b = c : d ⇔ ad = bc (product of extremes = product of means).
To combine a : b and b : c, scale both so the shared term matches, then read off a : b : c.
Mean proportional between a and b = √(ab). Third proportional to a and b = b²/a.
If a : b = 3 : 4, write the quantities as 3k and 4k and solve for k.
Componendo–dividendo: if a/b = c/d then (a + b)/(a − b) = (c + d)/(c − d).
Dividing an amount in the ratio a : b : c means shares of a/(a+b+c), b/(a+b+c) and c/(a+b+c) of the total.

Ratio and Proportion Practice Questions with Answers

Attempt each question first, then open the explanation. All 24 questions below are free to read and require no signup.

Q1.If a : b = 3 : 4 and b : c = 8 : 9, then a : c is:
Easy
- A1 : 2
- B2 : 3
- C3 : 4
- D4 : 5
+Show Answer & Explanation
Answer: B. 2 : 3
Explanation: a/c = (a/b)(b/c) = (3/4)(8/9) = 24/36 = 2 : 3.
Ratio and Proportion question 1 of 24
Q2.₹1,200 is divided between A and B in the ratio 3 : 5. B's share is:
Easy
- A₹450
- B₹600
- C₹700
- D₹750
+Show Answer & Explanation
Answer: D. ₹750
Explanation: B gets 5/8 of 1200 = ₹750.
Ratio and Proportion question 2 of 24
Q3.Two numbers are in the ratio 3 : 5. If each is increased by 10, the ratio becomes 5 : 7. The numbers are:
Moderate
- A9 and 15
- B12 and 20
- C15 and 25
- D18 and 30
+Show Answer & Explanation
Answer: C. 15 and 25
Explanation: (3x + 10)/(5x + 10) = 5/7 → 21x + 70 = 25x + 50 → x = 5 → 15 and 25.
Ratio and Proportion question 3 of 24
Q4.If x : y = 2 : 3, then (3x + 2y) : (2x + 3y) equals:
Moderate
- A11 : 12
- B12 : 13
- C13 : 14
- D14 : 15
+Show Answer & Explanation
Answer: B. 12 : 13
Explanation: Put x = 2, y = 3: (6 + 6) : (4 + 9) = 12 : 13.
Ratio and Proportion question 4 of 24
Q5.The mean proportional between 9 and 16 is:
Easy
- A10
- B12
- C12.5
- D14
+Show Answer & Explanation
Answer: B. 12
Explanation: √(9 × 16) = √144 = 12.
Ratio and Proportion question 5 of 24
Q6.The third proportional to 4 and 12 is:
Moderate
- A24
- B30
- C36
- D48
+Show Answer & Explanation
Answer: C. 36
Explanation: Third proportional = b²/a = 144/4 = 36.
Ratio and Proportion question 6 of 24
Q7.The ages of A and B are in the ratio 4 : 5 and their sum is 45 years. A's age is:
Easy
- A18 years
- B20 years
- C22 years
- D25 years
+Show Answer & Explanation
Answer: B. 20 years
Explanation: Total parts = 9 → 1 part = 5 years → A = 4 × 5 = 20 years.
Ratio and Proportion question 7 of 24
Q8.Three salaries are in the ratio 2 : 3 : 5 and total ₹40,000. The largest salary is:
Easy
- A₹16,000
- B₹18,000
- C₹20,000
- D₹24,000
+Show Answer & Explanation
Answer: C. ₹20,000
Explanation: Total parts = 10 → 1 part = ₹4,000 → largest = 5 × 4,000 = ₹20,000.
Ratio and Proportion question 8 of 24
Q9.If 4 : 6 = x : 9, then x equals:
Easy
- A5
- B6
- C7
- D8
+Show Answer & Explanation
Answer: B. 6
Explanation: Cross-multiplying: 6x = 36 → x = 6.
Ratio and Proportion question 9 of 24
Q10.₹900 is divided among A, B and C in the ratio 2 : 3 : 4. C's share is:
Easy
- A₹200
- B₹300
- C₹400
- D₹450
+Show Answer & Explanation
Answer: C. ₹400
Explanation: Total 9 parts → C gets 4/9 × 900 = ₹400.
Ratio and Proportion question 10 of 24
Q11.If a : b = 2 : 3 and b : c = 4 : 5, then a : b : c is:
Moderate
- A2 : 3 : 5
- B8 : 12 : 15
- C6 : 9 : 10
- D4 : 6 : 5
+Show Answer & Explanation
Answer: B. 8 : 12 : 15
Explanation: Scale b to match: a : b = 8 : 12 and b : c = 12 : 15 → 8 : 12 : 15.
Ratio and Proportion question 11 of 24
Q12.The ratio of two numbers is 5 : 8 and their difference is 24. The smaller number is:
Moderate
- A30
- B40
- C48
- D64
+Show Answer & Explanation
Answer: B. 40
Explanation: The 3-part difference equals 24 → 1 part = 8 → smaller = 5 × 8 = 40.
Ratio and Proportion question 12 of 24
Q13.If x : y = 3 : 4, then (x + y) : (y − x) is:
Moderate
- A1 : 7
- B7 : 1
- C3 : 4
- D4 : 3
+Show Answer & Explanation
Answer: B. 7 : 1
Explanation: Put x = 3 and y = 4: (3 + 4) : (4 − 3) = 7 : 1.
Ratio and Proportion question 13 of 24
Q14.The fourth proportional to 3, 6 and 8 is:
Moderate
- A12
- B14
- C16
- D24
+Show Answer & Explanation
Answer: C. 16
Explanation: 3 : 6 = 8 : x → 3x = 48 → x = 16.
Ratio and Proportion question 14 of 24
Q15.Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, the ratio becomes 12 : 23. The smaller number is:
Difficult
- A27
- B33
- C45
- D55
+Show Answer & Explanation
Answer: B. 33
Explanation: (3x − 9)/(5x − 9) = 12/23 → 69x − 207 = 60x − 108 → 9x = 99 → x = 11, so the smaller number is 33.
Ratio and Proportion question 15 of 24
Q16.If 20% of A equals 30% of B, then A : B is:
Moderate
- A2 : 3
- B3 : 2
- C4 : 5
- D5 : 4
+Show Answer & Explanation
Answer: B. 3 : 2
Explanation: 0.2A = 0.3B → A/B = 0.3/0.2 = 3/2.
Ratio and Proportion question 16 of 24
Q17.Simplify the ratio 18 : 24.
Easy
- A2 : 3
- B3 : 4
- C4 : 5
- D6 : 8
+Show Answer & Explanation
Answer: B. 3 : 4
Explanation: Dividing both by 6 gives 3 : 4.
Ratio and Proportion question 17 of 24
Q18.₹600 is divided between two people in the ratio 1 : 2. The larger share is:
Easy
- A₹200
- B₹300
- C₹400
- D₹450
+Show Answer & Explanation
Answer: C. ₹400
Explanation: Total 3 parts → larger = 2/3 × 600 = ₹400.
Ratio and Proportion question 18 of 24
Q19.If 3 : 5 = 12 : x, then x equals:
Easy
- A15
- B18
- C20
- D25
+Show Answer & Explanation
Answer: C. 20
Explanation: Cross-multiplying: 3x = 60 → x = 20.
Ratio and Proportion question 19 of 24
Q20.The ratio of two numbers is 4 : 7 and their sum is 66. The larger number is:
Moderate
- A24
- B35
- C42
- D44
+Show Answer & Explanation
Answer: C. 42
Explanation: Total 11 parts → 1 part = 6 → larger = 7 × 6 = 42.
Ratio and Proportion question 20 of 24
Q21.If a : b = 1 : 2 and b : c = 3 : 4, then a : c is:
Moderate
- A1 : 4
- B3 : 8
- C2 : 3
- D3 : 4
+Show Answer & Explanation
Answer: B. 3 : 8
Explanation: a/c = (1/2)(3/4) = 3/8.
Ratio and Proportion question 21 of 24
Q22.The mean proportional between 4 and 25 is:
Moderate
- A8
- B10
- C12.5
- D14.5
+Show Answer & Explanation
Answer: B. 10
Explanation: √(4 × 25) = √100 = 10.
Ratio and Proportion question 22 of 24
Q23.If x : y = 5 : 6, then (2x + y) : (x + 2y) is:
Difficult
- A16 : 17
- B3 : 4
- C4 : 5
- D5 : 6
+Show Answer & Explanation
Answer: A. 16 : 17
Explanation: Put x = 5 and y = 6: (10 + 6) : (5 + 12) = 16 : 17.
Ratio and Proportion question 23 of 24
Q24.Divide 84 in the ratio 3 : 4. The smaller part is:
Easy
- A28
- B36
- C42
- D48
+Show Answer & Explanation
Answer: B. 36
Explanation: Total 7 parts → 1 part = 12 → smaller = 3 × 12 = 36.
Ratio and Proportion question 24 of 24

Ratio and Proportion — Frequently Asked Questions

How do I combine two ratios that share a term?+

If a : b = 3 : 4 and b : c = 8 : 9, scale the first by 2 so b matches: a : b = 6 : 8 and b : c = 8 : 9, giving a : b : c = 6 : 8 : 9.

What is a mean proportional?+

The mean proportional between a and b is √(ab) — the number x for which a : x = x : b. Between 9 and 16 it is 12.

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