UPSC Prelims 2002 Q63: Science & Technology – Quantitative Aptitude
The age of a man is three times the sum of the ages of his two sons. Five years hence, his
age will be double the sum of the ages of his sons. The father’s present age is
- (a) 40 years
- (b) 45 years
- (c) 50 years
- (d) 55 years
Answer: (b) 45 years
Explanation
Father's present age from the ages of the sons
| Step | Working |
|---|---|
| Let the sons' ages total S | Father's age = 3S |
| Five years later | Father's age = 3S + 5; the sons' total = S + 10 |
| Condition | 3S + 5 = 2(S + 10) |
| Solve | S = 15, so the father's age is 45 years |
With the sum of the sons' ages S, the father is 3S. After five years the father is 3S + 5 and the two sons together are S + 10. Setting 3S + 5 = 2S + 20 gives S = 15, so the father is 45 years old.
Answer: (b) 45 years.
Why each option is right or wrong
- (a) Incorrect. 40 years would make S about 13.3 and the condition fails.
- (b) CORRECT. 45 = 3 × 15 and 50 = 2 × 25.
- (c) Incorrect. 50 years would make S about 16.7 and the condition fails.
- (d) Incorrect. 55 years would make S about 18.3 and the condition fails.
Key point
Each son adds 5 years, so two sons add 10 years to their sum, not 5.
Remember
Two sons: the sum rises by 10 in five years.
Common mistakes
- Adding 5 to the sons' sum instead of 10.
- Using the father's age as double, not triple.
- Solving for S and stopping there without tripling it.
Exam tip
Test an option: 45 → S = 15 → after 5 years 50 and 2 × 25 = 50.
Sources
- NCERT Class X Mathematics — Linear equations in two variables
- Arun Sharma — How to Prepare for Quantitative Aptitude for the CAT (Algebra: problems on ages)