A race with a head start — Aptitude Question
A race with a head start: In a 100 m race A beats B by 10 metres. If A's speed is 10 m/s, what is B's speed? Answer and worked solution on CodeKairo.
- Topic: Time, Speed & Distance
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
In a 100 m race A beats B by 10 metres. If A's speed is 10 m/s, what is B's speed?
Options
- 8 m/s
- 9 m/s
- 9.5 m/s
- 10 m/s
Show the answer and the worked solution
Correct answer: B. 9 m/s
Worked solution
- A takes 100 ÷ 10 = 10 seconds.
- In 10 seconds B covers 90 m.
- B's speed = 90 ÷ 10 = 9 m/s.
Answer: 9 m/s.
The idea
'Beats by 10 metres' means that when the winner finishes, the loser is 10 m short. Both are compared over the same time, not the same distance.
Shortcut. In the same time the distances are in the ratio of the speeds, 100 : 90, so B runs at 0.9 × 10 = 9 m/s.
Common trap. 10 m/s comes from dividing the full 100 m by A's 10 s, which is A's own speed; when A finishes, B has covered only 90 m, so B's speed is 90 ÷ 10 = 9 m/s.