CAPF AC 2022 Q30: General Mental Ability – Quantitative Aptitude
- (a) 30 years
- (b) 27 years
- (c) 28 years
- (d) 29 years
Answer: (c) 28 years
Explanation
Average age of a father and two sons
Given: the average age of the father and elder son is 35, of the father and younger son is 32, and of the two sons is 17; find the average age of all three.
How to think: turn each average into a sum.
Add the three sums.
Each person is then counted twice.
| Pair | Average | Sum |
|---|---|---|
| Father + elder son | 35 | 70 |
| Father + younger son | 32 | 64 |
| Elder son + younger son | 17 | 34 |
| Total of the three sums | All three pairs | 168 |
Sum of the three ages: 168 ÷ 2 = 84.
Average of the three: 84 ÷ 3 = 28 years.
Extra check: father = 84 − 34 = 50, elder son = 20, younger son = 14.
Answer: (c) 28 years.
Why each option is right or wrong
- (a) Incorrect. 30 years would need a total of 90, but the three ages add up to 84.
- (b) Incorrect. 27 years would need a total of 81.
- (c) CORRECT. The three ages total 84, so the average is 28 years.
- (d) Incorrect. 29 years would need a total of 87.
Key point
Pair averages given: convert to sums, add, halve to get the total of all three, then divide by 3. Shortcut: the answer is the average of the three pair averages: (35 + 32 + 17) ÷ 3 = 28.
Remember
Average of the three pair averages = 28.
Common mistakes
- Forgetting to halve the total of 168 because each person is counted twice.
- Adding the averages 35 + 32 + 17 and dividing by 2 instead of 3.
- Treating the averages as sums without multiplying each by 2.
Exam tip
Educated guess: simply take the average of the three averages: 35 + 32 + 17 = 84, and 84 ÷ 3 = 28. It works because each person appears in exactly two pairs.
Sources
- NCERT Class VII Mathematics — Data Handling (arithmetic mean)
- R. S. Aggarwal, Quantitative Aptitude — Average and Problems on Ages