Problems on Ages for SSC CGL: The Short Answer
Age questions turn into one or two simple equations. Write the present ages as ratio parts (5x and 3x) or as one unknown (S and 3S), add the same number of years to every person for a future age, subtract it for a past age, and solve. The key fact: the difference between two people's ages never changes.
Key takeaway for SSC: When the options are given, putting each option back into the question is often faster than solving: an answer must satisfy every condition. Every result on this page was checked with a program.
Age questions appear in the quantitative sections of SSC CGL, SSC CHSL, SSC MTS, SSC GD and SSC CPO, usually as ratio questions. For the ratio basics behind them, see ratio and proportion for SSC CGL.
Age Formulas and Rules
| Situation | How to write it |
|---|---|
| Present ages in ratio a : b | ax and bx |
| n years hence | ax + n and bx + n |
| n years ago | ax − n and bx − n |
| A is k times B | A = kB |
| Difference of ages | stays the same at every time |
| Ratio changes from a : b to c : d after n years | x = n(d − c) ÷ (bc − ad) |
Problems on Ages: Solved Examples
Example 1: Ratio now and after some years
The ratio of the present ages of A and B is 5 : 3. After 6 years it will be 3 : 2. Find their present ages.
- (5x + 6) ÷ (3x + 6) = 3 ÷ 2, so 10x + 12 = 9x + 18 and x = 6.
- A = 30 years, B = 18 years. Check: after 6 years, 36 : 24 = 3 : 2.
Example 2: Sum of ages and years ago
The sum of the present ages of two brothers is 56 years. Four years ago their ages were in the ratio 5 : 3. Find their present ages.
- Four years ago the sum was 56 − 8 = 48, so 5k + 3k = 48 and k = 6.
- Ages then: 30 and 18. Present ages: 34 and 22 years.
Example 3: Times-older question
A father is three times as old as his son. After 12 years he will be twice as old as his son. Find the son's present age.
- 3S + 12 = 2(S + 12), so S = 12 years and the father is 36.
Example 4: Ratio and difference
Two ages are in the ratio 4 : 7 and differ by 15 years. The difference is 3 parts, so 1 part = 5. Ages: 20 and 35 years.
Example 5: Product of ages
A is 5 years older than B, and the product of their present ages is 266. Try factor pairs that differ by 5: 14 × 19 = 266. B = 14 years, A = 19 years.
Option-Checking Trick
In Example 1, if the options for A's age were 25, 30, 35 and 40, test each with ratio 5 : 3:
- A = 30 → B = 18 → after 6 years 36 : 24 = 3 : 2 ✔
- A = 25 → B = 15 → 31 : 21 ✘
Only one option passes every condition.
Common Mistakes in Age Questions
- Adding the years to only one person.
- Using the present ratio for a past or future time.
- Forgetting that the difference of ages is constant.
- Reporting x instead of the actual age (5x).
Problems on Ages Practice Questions with Answers
- The present ages of A and B are in the ratio 7 : 4 and their sum is 77 years. Find their ages. Answer: 49 and 28 years.
- Four years ago A was twice as old as B. After 4 years the ratio of their ages will be 5 : 3. Find their present ages. Answer: A = 36, B = 20 years.
- A mother is four times as old as her daughter. In 6 years she will be two and a half times as old. Find their present ages. Answer: mother 24, daughter 6 years.
- The average age of A, B and C is 30 years and their ages are in the ratio 2 : 3 : 5. Find their ages. Answer: 18, 27 and 45 years.
For timed practice, take the SSC GD Ratio and Proportion Mock Test 03 and the SSC CHSL Problems on Ages Mock Test 01.
Problems on Ages FAQs
What is the fastest method for age questions?
Write the present ages as ratio parts, add or subtract the same years for everyone, and solve the one equation. When options are given, test them in the question.
Does the difference between two ages change over time?
No. If A is 12 years older than B today, A is 12 years older at every point in time.
Are age questions asked in SSC MTS and SSC GD?
Yes. Ratio-based age questions appear in the maths sections of SSC MTS, SSC GD, SSC CHSL, SSC CGL and SSC CPO.
Practice Next
- Topic tests: SSC GD Ratio and Proportion Mock Test 03, SSC CHSL Problems on Ages Mock Test 01, SSC CGL Problems on Ages Mock Test 02 and SSC MTS Ratio and Proportion Mock Test 02.
- Related notes: ratio and proportion for SSC CGL, average tricks for SSC CGL and percentage tricks for SSC CGL.
- Browse all study notes.