Cyclist and motorcycles relative speed
CAT 2019 Slot 2 · Quantitative Ability · Medium · Speed, Time & distance
This is a medium Quantitative Ability question from the CAT 2019 Slot 2 paper. It tests Speed, Time & distance. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.
A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motorcycle leaves A and moves towards B. Forty-five such motorcycles reach B by 11 am. All motorcycles have the same speed. If the cyclist had doubled his speed, how many motorcycles would have reached B by the time the cyclist reached B?
- A.
22
- B.
20
- C.
15
- D.
23
C
Explanation
The cyclist takes 60 minutes (10 am to 11 am) to travel from A to B.
45 motorcycles leave between 10:01 am and 10:45 am. The 45th motorcycle reaches B at 11:00 am. Since it left at 10:45 am, each motorcycle takes minutes to reach B.
If the cyclist doubles his speed, he will take 30 minutes and reach B at 10:30 am.
To reach B by 10:30 am, a motorcycle must leave A at or before am.
Motorcycles leaving from 10:01 am to 10:15 am arrive by 10:30 am. Total count .
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