CAPF AC 2022 Q5: General Mental Ability – Quantitative Aptitude
A runner's average speed reduces by 25% every hour. If he runs 16 km in the first hour and he runs for 3 hours, then what is his overall average speed?
- (a) 12 km/hr
- (b) 12.33 km/hr
- (c) 10.33 km/hr
- (d) 13 km/hr
Answer: (b) 12.33 km/hr
Explanation
Average speed of a tiring runner
Given: a runner's speed reduces by 25% every hour; he runs 16 km in the first hour and runs for 3 hours; find his overall average speed.
How to think: average speed = total distance ÷ total time.
Find the distance in each hour first.
| Hour | Working | Distance |
|---|---|---|
| First | Given | 16 km |
| Second | 16 × 0.75 | 12 km |
| Third | 12 × 0.75 | 9 km |
| Total | 16 + 12 + 9 | 37 km |
Average speed: 37 km ÷ 3 hours = 12.33 km/hr.
Answer: (b) 12.33 km/hr.
Why each option is right or wrong
- (a) Incorrect. 12 km/hr is only the speed of the second hour.
- (b) CORRECT. 37 km in 3 hours gives 12.33 km/hr.
- (c) Incorrect. 10.33 km/hr would mean only 31 km in three hours.
- (d) Incorrect. 13 km/hr would need 39 km in three hours.
Key point
Average speed = total distance ÷ total time. A 25% fall each hour means multiply by 3/4: 16 → 12 → 9.
Remember
16 + 12 + 9 = 37 km in 3 hours.
Common mistakes
- Reducing by 25% of the first hour's speed each time (16, 12, 8).
- Taking the middle value of 12 km/hr as the average without adding up.
- Dividing the total by 2 instead of by the 3 hours run.
Exam tip
Educated guess: the three hourly speeds are 16, 12 and 9. The first is 4 above 12 but the last is only 3 below it, so the average is a little above 12.
Sources
- NCERT Class VII Science and Mathematics — Motion and Time; Comparing Quantities (percentage decrease)
- R. S. Aggarwal, Quantitative Aptitude — Time and Distance