Late at one speed, early at another — Aptitude Question
Late at one speed, early at another: Walking at 4 km/h a man reaches his office 10 minutes late; at 6 km/h he… Answer and worked solution on CodeKairo.
- Topic: Time, Speed & Distance
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 120 seconds
Question
Walking at 4 km/h a man reaches his office 10 minutes late; at 6 km/h he arrives 5 minutes early. How far is the office?
Options
- 2 km
- 3 km
- 4 km
- 5 km
Show the answer and the worked solution
Correct answer: B. 3 km
Worked solution
- Time difference = 15 min = 1/4 hour.
- d/4 − d/6 = 1/4 → d(3 − 2)/12 = 1/4 → d/12 = 1/4.
- d = 3 km.
- Check: 45 min at 4 km/h and 30 min at 6 km/h, a difference of 15 min. ✓
Answer: 3 km.
The idea
Late by a and early by b means the two trips differ by (a + b) in time. The scheduled arrival time never has to be found.
Shortcut. Distance = (product of speeds ÷ difference of speeds) × time gap = (24 ÷ 2) × ¼ h = 3 km.
Common trap. 2 km — taking the time gap as the 10 minutes late alone and ignoring the 5 minutes early; the two trips differ by 15 minutes.