Ten minutes late, five minutes early — Aptitude Question
Ten minutes late, five minutes early: 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: 90 seconds
Question
Walking at 4 km/h a man reaches his office 10 minutes late; at 6 km/h he reaches 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 between the two speeds = 10 + 5 = 15 min = 1/4 h.
- d/4 − d/6 = 1/4 → d(3 − 2)/12 = 1/4 → d/12 = 1/4 → d = 3 km.
- Check: 3/4 h = 45 min and 3/6 h = 30 min, 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. Set d/s₁ − d/s₂ equal to that difference; the fixed 'on-time' moment never needs to be found.
Shortcut. Speeds 4 : 6 make times 3 : 2; the one-part difference is the 15-minute gap, so the slow walk is 3 parts = 45 min = ¾ h, and ¾ × 4 = 3 km.
Common trap. 2 km — taking the gap as the 10 minutes late alone and ignoring the 5 minutes early; 2 km gives trips of 30 and 20 minutes, only 10 apart.