CAPF AC 2022 Q42: General Mental Ability – Quantitative Aptitude
Two friends 10 km apart start running towards each other at speeds of 10 km/hr and 14 km/hr respectively. After how much time will they meet each other?
- (a) 20 minutes
- (b) 25 minutes
- (c) 28 minutes
- (d) 30 minutes
Answer: (b) 25 minutes
Explanation
Two runners approaching each other
Given: two friends 10 km apart run towards each other at 10 km/hr and 14 km/hr; find when they meet.
How to think: when two bodies move towards each other, the gap closes at the sum of their speeds.
| Step | Working |
|---|---|
| Closing speed | 10 + 14 = 24 km/hr |
| Distance to close | 10 km |
| Time | 10 ÷ 24 hour = 5/12 hour |
| In minutes | 5/12 × 60 = 25 minutes |
Check: in 25 minutes the first runs about 4.17 km and the second about 5.83 km.
Together that is 10 km.
Answer: (b) 25 minutes.
Why each option is right or wrong
- (a) Incorrect. In 20 minutes they cover only 8 km between them.
- (b) CORRECT. 10 km at a closing speed of 24 km/hr takes 25 minutes.
- (c) Incorrect. In 28 minutes they would cover 11.2 km, more than the gap.
- (d) Incorrect. In 30 minutes they would cover 12 km, more than the gap.
Key point
Opposite directions (towards or away): relative speed = sum. Same direction: relative speed = difference. Time to meet = distance ÷ relative speed.
Remember
Towards each other: add the speeds.
Common mistakes
- Using the difference of the speeds (4 km/hr), which applies to the same direction.
- Dividing 10 km by one runner's speed only.
- Forgetting to convert the fraction of an hour into minutes.
Exam tip
Educated guess: at 24 km/hr they would close 12 km in half an hour. The gap is only 10 km, so the time is a little less than 30 minutes; 25 fits.
Sources
- NCERT Class VII Science — Motion and Time
- R. S. Aggarwal, Quantitative Aptitude — Time and Distance (relative speed)