UPSC Prelims 2002 Q78: Science & Technology – Quantitative Aptitude
A bus is moving at 30 km/h, and a car is coming from behind at 50 km/h. How far apart are
they if it takes 15 minutes for the car to catch up with the bus?
- (a) 5 km
- (b) 7.5 km
- (c) 12.5 km
- (d) 15 km
Answer: (a) 5 km
Explanation
Distance between a bus and a car catching up
| Quantity | Value |
|---|---|
| Speed of the bus | 30 km/h |
| Speed of the car | 50 km/h |
| Relative speed | 50 − 30 = 20 km/h |
| Time to catch up | 15 minutes = 0.25 hour |
A bus is moving at 30 km/h and a car is coming from behind at 50 km/h, so the car catches up with the bus after 15 minutes. The car gains 20 km on the bus every hour. In 15 minutes (0.25 hour) it gains 20 × 0.25 = 5 km, so the distance between them is 5 km.
Answer: (a) 5 km.
Why each option is right or wrong
- (a) CORRECT. 20 km/h × 0.25 h = 5 km.
- (b) Incorrect. 7.5 km would need 22.5 minutes at 20 km/h.
- (c) Incorrect. 12.5 km would need 37.5 minutes at 20 km/h.
- (d) Incorrect. 15 km would need 45 minutes at 20 km/h.
Key point
When two bodies move in the same direction, the gap closes at the difference of speeds.
Remember
Same direction: subtract the speeds.
Common mistakes
- Using the sum of the speeds (80 km/h) as for opposite directions.
- Taking 15 minutes as 15 hours in the distance formula.
- Multiplying by the car's speed (12.5 km).
Exam tip
Relative speed 20 km/h × 1/4 hour = 5 km.
Sources
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Time and Distance)
- Arun Sharma — How to Prepare for Quantitative Aptitude for the CAT (Time, Speed and Distance)