CAPF AC 2020 Q125: General Mental Ability – Quantitative Aptitude
- (a) 2 years
- (b) 3 years
- (c) 4 years
- (d) 5 years
Answer: (d) 5 years
Explanation
Ages of A and B
Given: two years ago, the age of A was three times the age of B.
B is currently 9 years old.
We need the number of years after which the age of A will be double the age of B.
How to think: work in three steps: two years ago, now, and later.
| Time | Age of B | Age of A |
|---|---|---|
| Two years ago | 9 − 2 = 7 | 3 × 7 = 21 |
| Now | 9 | 21 + 2 = 23 |
| After x years | 9 + x | 23 + x |
Equation: 23 + x = 2 × (9 + x).
So 23 + x = 18 + 2x, which gives x = 5.
Check: after 5 years A is 28 and B is 14.
28 is double of 14.
Shortcut: the gap in ages is always 23 − 9 = 14.
A is double of B when B's age equals the gap, that is when B is 14.
B is 9 now, so that is 5 years away.
Answer: (d) 5 years.
Why each option is right or wrong
- (a) Incorrect. After 2 years the ages are 25 and 11; 25 is not double of 11.
- (b) Incorrect. After 3 years the ages are 26 and 12; 26 is not double of 12.
- (c) Incorrect. After 4 years the ages are 27 and 13; 27 is not double of 13.
- (d) CORRECT. After 5 years the ages are 28 and 14, and 28 is double of 14.
Key point
Two years ago: B = 7, A = 21. Now: B = 9, A = 23. A is double when B's age equals the age gap (14), which is 5 years from now.
Remember
A is twice B when B's age equals the difference in their ages.
Common mistakes
- Taking A as three times B's present age, 27.
- Forgetting to add the two years back to A's age.
- Counting the years from two years ago instead of from now.
Exam tip
Educated guess: the age gap never changes. One person is double the other exactly when the younger one's age equals the gap.
Sources
- NCERT Class VIII Mathematics — Linear Equations in One Variable (age problems)
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Problems on Ages)