A worker reaches his factory 3 minutes late if his speed from his house to the factory is 5 km/hr. If he walks at a speed of 6 km/hr, then he reaches the factory 7 minutes early. The distance of the factory from his house is
- (a) 3 km
- (b) 4 km
- (c) 5 km ✓ UPSC's answer
- (d) 6 km
Why the answer is (c)
• Let the distance be d km and the scheduled travel time be T hours.
• At 5 km/hr, time taken is d/5, which is 3 minutes late, so d/5 = T + 3/60.
• At 6 km/hr, time taken is d/6, which is 7 minutes early, so d/6 = T - 7/60.
• Subtracting gives d/5 - d/6 = 3/60 + 7/60 = 10/60 = 1/6 hour.
• Thus d/30 = 1/6, so d = 5 km, which is option (c).
Why the other options are wrong
- (a) 3 km
- For 3 km, the time difference between 5 km/hr and 6 km/hr is 6 minutes, not the required 10 minutes.
- (b) 4 km
- For 4 km, the time difference between 5 km/hr and 6 km/hr is 8 minutes, not the required 10 minutes.
- (d) 6 km
- For 6 km, the time difference between 5 km/hr and 6 km/hr is 12 minutes, not the required 10 minutes.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2014, held on 24 August 2014. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.