CAPF AC 2020 Q115: General Mental Ability – Quantitative Aptitude
The average age of the boys in a class is 12 years. The average age of the girls in the class is 11 years. There are 50% more girls than boys in the class. Which one of the following is the average age of the class (in years)?
- (a) 11.2 years
- (b) 11.4 years
- (c) 11.6 years
- (d) 11.8 years
Answer: (b) 11.4 years
Explanation
Average age of a class
Given: the average age of the boys is 12 years and of the girls is 11 years.
There are 50% more girls than boys.
How to think: pick easy numbers.
If there are 2 boys, 50% more means 3 girls.
There are more girls, so the class average must lie nearer to 11 than to 12.
| Group | Number | Average age | Total age |
|---|---|---|---|
| Boys | 2 | 12 years | 24 |
| Girls | 3 | 11 years | 33 |
| Class | 5 | ? | 57 |
Average age of the class = 57 ÷ 5 = 11.4 years.
Check by the balance method:
| Point | Detail |
|---|---|
| Gap between the averages | 12 − 11 = 1 year |
| Boys are | 2 parts out of 5 |
| Average | 11 + (2 ÷ 5) × 1 = 11.4 |
Answer: (b) 11.4 years.
Why each option is right or wrong
- (a) Incorrect. 11.2 would need four girls for every boy.
- (b) CORRECT. (2 × 12 + 3 × 11) ÷ 5 = 57 ÷ 5 = 11.4 years.
- (c) Incorrect. 11.6 is nearer to 12; it would mean more boys than girls.
- (d) Incorrect. 11.8 is far too close to the boys' average.
Key point
Weighted average = (n1 × a1 + n2 × a2) ÷ (n1 + n2). Boys : girls = 2 : 3, so average = (24 + 33) ÷ 5 = 11.4.
Remember
The average leans towards the bigger group.
Common mistakes
- Taking the simple average of 12 and 11 to get 11.5.
- Reading 50% more girls as girls being half of the boys.
- Swapping the weights and getting 11.6.
Exam tip
Educated guess: more girls means the average is below 11.5. That leaves 11.2 and 11.4.
Sources
- NCERT Class VII Mathematics — Data Handling (arithmetic mean)
- NCERT Class IX Mathematics — Statistics (mean)