Cyclist and motorcycles relative speed

CAT 2019 Slot 2 · QA · Medium · Speed, Time & distance

All CAT 2019 Slot 2 questionsMore Speed, Time & distance questionsAll CAT QA

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?

  1. A.

    22

  2. B.

    20

  3. C.

    15

  4. D.

    23

Answer

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 11:00−10:45=1511:00 - 10:45 = 15 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 10:30−15=10:1510:30 - 15 = 10:15 am.

Motorcycles leaving from 10:01 am to 10:15 am arrive by 10:30 am. Total count =15= 15.

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace