Question

A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motor cycle leaves A and moves towards B. Forty-five such motor cycles reach B by 11 am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached B by the time the cyclist reached B?

• A. 23
• B. 20
• C. 15
• D. 22

Answer 1

Answer: (C)

15

Answer 2

The cyclist takes 60 minutes to cover the distance AB. Starting from 10:01 am, a motorcycle departs from point A every minute, all moving towards B at the same speed. Forty-five motorcycles, including the 45th one that started at 10:45 am, reach B by 11 am, precisely at that time. This implies that the rest of the motorcycles arrived at B before 11 am. Therefore, each motorcycle requires 15 minutes to cover the distance AB.
If the cyclist doubles his speed, he will reach B in 30 minutes, which is at 10:30 am. Consequently, the 15th motorcycle, departing from A at 10:15 am, will be the last one to reach point B at 10:30 am. Hence, by the time the cyclist arrives at B, a total of 15 motorcycles will have reached B.