Age Ratio-Based Problems: 12 Questions with Step-by-Step Solutions

Solve 12 age ratio-based questions from the KnowledgeGate practice bank. Each fresh solution shows how to form the equation, shift every age correctly, and verify the answer.

KnowledgeGate Team

Exam prep & CS education

18 Oct 20267 min read

Age ratios look easy until the ages move into the past or future. Students often change only one person's age, or mistake the difference between ratio parts for an age difference. The arithmetic is usually short once the model is correct. KnowledgeGate has at least 40 published questions on Age Ratio-Based Problems in Aptitude. This set gives exactly 12, ordered from direct equations to past, future and three-person problems. Before each solution, choose an option and write one equation. That pause tests whether you can translate the words yourself clearly.

The age-ratio method to use before the questions

Every person's age changes by the same number of years. Therefore, the age difference stays constant, although the ratio usually changes. If a present ratio is a:b, write the ages as ax and bx. Then use the given sum, difference, average or shifted ratio to find x. Always name the time frame.

For example, A and B are in the ratio 5:3 and differ by 12 years. Let their ages be 5x and 3x. Then 5x - 3x = 12, so 2x = 12 and x = 6. Their present ages are 30 and 18. Six years later, they are 36 and 24, giving 36:24 = 3:2.

Adding 6 directly to the ratio parts would give 11:9, which is wrong. The numbers 5 and 3 are parts, not ages. Use (ax + t):(bx + t) for t years later and (ax - t):(bx - t) for t years ago. If the average of two ages is m, their sum is 2m.

Age ratio questions 1-3: direct ratios and one future equation

Labels below are bank attributions.

Question 1

BPSC 2023

The ratio of the ages of two brothers is 4 : 3. If the elder brother is 6 years older than the younger one, then their ages (in years) are

(a) 24, 18
(b) 36, 30
(c) 15, 9
(d) More than one of the above
(e) None of the above

Answer: (a) 24, 18.

Let the ages be 4x and 3x. From 4x - 3x = 6, x = 6, giving 24 and 18. Both 24:18 = 4:3 and 24 - 18 = 6 check.

Question 2

TCS 2024

Jack, twenty one years old, is three times as old as his brother. How old will Jack be when he is twice as old as his brother?

(a) 24
(b) 28
(c) 32
(d) 36

Answer: (b) 28.

Jack's brother is 21 ÷ 3 = 7. Solve 21 + t = 2(7 + t) to get t = 7. Jack will be 28 and his brother 14, with the same 14-year gap.

Question 3

Wipro 2024

Present age of Vinod and Ashok are in ratio of 3:4 respectively. After 5 years, the ratio of their ages becomes 7:9 respectively. What is Ashok’s present age is ?

(a) 40 years
(b) 28 years
(c) 32 years
(d) 36 years

Answer: (a) 40 years.

Let the ages be 3x and 4x. Cross-multiplying (3x + 5)/(4x + 5) = 7/9 gives x = 10. Ashok is 4x = 40; the future ratio is 35:45 = 7:9.

Age ratio questions 4-6: sums, past ratios and a known future age

Question 4

TCS 2024

The ratio of the ages of Meena and Meera is 4 : 3. The sum of their ages is 28 years. The ratio of their ages after 8 years will be

(a) 4 : 3
(b) 6 : 5
(c) 7 : 4
(d) 12 : 11

Answer: (b) 6 : 5.

From 4x + 3x = 28, x = 4, giving 16 and 12. Eight years later, 24:20 = 6:5. Keeping the present 4:3 ratio would be wrong.

Question 5

UGC NET 2020

Mr X is 40 years old and Mr Y is 60 years old. How many years ago was the ratio of their ages 3:5?

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

Answer: (b) 10 years.

Solve (40 - t)/(60 - t) = 3/5. Cross-multiplication gives t = 10. Both ages decrease to 30 and 50, and 30:50 = 3:5.

Question 6

Deloitte 2025

At present, the ratio between the ages of Amit and Dhiraj is 5 : 4. After 6 years, Amit’s age will be 26 years. What is the age of Dhiraj at present?

(a) 12 years
(b) 16 years
(c) 19 ½ years
(d) 21 years

Answer: (b) 16 years.

Amit is now 26 - 6 = 20. Five ratio parts equal 20, so one part is 4. Dhiraj's age is 4 × 4 = 16. Shift time before scaling the ratio.

Age ratio questions 7-9: age differences and multi-person equations

Question 7

DSSSB 2024

The ratio of Amit’s and Ankit’s present age is 10 : 13. Amit is 18 years younger than Ankit. What will be the ratio of Amit’s age to Ankit’s age after 12 years?

(a) 4 : 5
(b) 3 : 5
(c) 4 : 9
(d) 4 : 7

Answer: (a) 4 : 5.

Let the ages be 10x and 13x. From 3x = 18, x = 6, giving 60 and 78. After 12 years, 72:90 = 4:5.

Question 8

TCS 2025

The sum of the ages of husband and wife at present is 60. Four years ago the ratio of their ages was 7 : 6. What is the age of the husband ?

(a) 28 years
(b) 32 years
(c) 42 years
(d) 38 years

Answer: (b) 32 years.

Four years ago, use 7x and 6x. Now 13x + 8 = 60, so x = 4. The husband is 7(4) + 4 = 32. Check: 28:24 = 7:6.

Question 9

SSC CGL 2024

At present, A is thrice as old as B. C is 5 years elder than B. The sum of the ages of A, B, C is 75 years. The ratio of the age of B five years ago to the age of A three years from now is:

(a) 2 : 3
(b) 1 : 4
(c) 4 : 7
(d) 1 : 5

Answer: (d) 1 : 5.

Set A = 3B, C = B + 5. From 3B + B + (B + 5) = 75, B = 14, A = 42 and C = 19. The requested ratio is (14 - 5):(42 + 3) = 9:45 = 1:5.

Age ratio questions 10-12: past/future checks and three-age systems

Question 10

UPTET 2019

The sum of the present ages of father and son is 68 years.
8 years ago, the ratio of their ages was 12 : 1.
The ratio of their ages after 4 years will be

(a) 16 : 5
(b) 13 : 2
(c) 15 : 4
(d) 14 : 3

Answer: (c) 15 : 4.

Eight years ago, use 12x and x. Now 13x + 16 = 68, so x = 4, giving 56 and 12. Four years later, 60:16 = 15:4.

Question 11

Wipro 2024

The present ages of A, B and C are in proportions 4:5:9. Nine years ago, sum of their ages was 45 years. Find their present ages in years.

(a) 15, 20, 35
(b) 20, 24, 36
(c) 20, 25, 45
(d) 16, 20, 36

Answer: (d) 16, 20, 36.

Present ages are 4x, 5x, 9x. Nine years ago, 18x - 27 = 45, so x = 4, giving 16, 20 and 36. Check: 7 + 11 + 27 = 45.

Question 12

TCS 2025

Twice the age of X is thrice the age of Y. 8 years back, the difference between the ages of X and Y was 18 years. What is the present age of X?

(a) 24
(b) 54
(c) 56
(d) 91

Answer: (b) 54.

From 2X = 3Y, X = 1.5Y. Since X - Y = 18, 0.5Y = 18, giving Y = 36 and X = 54. Check: 2 × 54 = 3 × 36 = 108.

The traps these 12 age-ratio questions expose

Trap	Questions	What to do
Ratio parts are not years	Q1, Q7	Use the stated difference to find one part.
Shift every person by the same `t`	Q2, Q3, Q4, Q5	Add or subtract `t` from every age before forming the new ratio.
Translate the correct time first	Q6, Q8, Q10	Move known ages to the time used by the equation.
Subtract years once per person; differences stay invariant	Q9, Q11, Q12	Count one shift for each person, and keep the age gap unchanged.

Use a 45-second check. Label present ages, mark past shifts minus and future shifts plus, and write both shifted ages before cross-multiplying. Substitute into the original ratio or sum. Reject negative ages or a changed age difference.

Use Aptitude for Placements: Section Topics and Weekly Plan for syllabus order and Aptitude for Placements: A 30-Day Practice Routine for timed practice.

What to practise next after this age-ratio set

Redo Questions 3, 5, 8, 9, 10 and 12 without looking at the solutions. Together, they test a changed ratio, a past ratio, a past ratio with a present sum, a three-person equation, two time shifts and an invariant difference.

Placement-focused readers can continue with Aptitude for Placement, while GATE-focused readers can use Aptitude for GATE Exam for structured aptitude preparation. The short version is simple: represent present ages first, move every person through time by the same number, and check the final values in the sentence that supplied the ratio.