Travelling at a fraction of the usual speed — Aptitude
Travelling at a fraction of the usual speed: Walking at three-quarters of his usual speed, a man reaches his office… Answer and worked solution on CodeKairo.
- Topic: Time, Speed & Distance
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
Walking at three-quarters of his usual speed, a man reaches his office 20 minutes late. What is his usual time for the journey?
Options
- 45 min
- 60 min
- 75 min
- 90 min
Show the answer and the worked solution
Correct answer: B. 60 min
Worked solution
- Speed × time is constant, so at 3/4 speed the time becomes 4/3 of usual.
- Extra time = (4/3 − 1) × usual = (1/3) × usual = 20 min.
- Usual time = 60 minutes.
Answer: 60 min.
The idea
At a fraction a/b of the usual speed the time becomes b/a of usual. The delay is the difference from 1, so the usual time follows in one step.
Shortcut. Back-substitute: 60 min at 3/4 speed becomes 60 × 4/3 = 80 min — exactly 20 minutes late.
Common trap. 75 min comes from taking the delay as a quarter of the usual time because the speed fell by a quarter: 20 × 4 = 80 min, nearest option 75. At 3/4 speed the time is 4/3 of usual, so the delay is a third of it: 20 × 3 = 60 min.