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 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?
Updated On: Jul 28, 2025
- 23
- 20
- 15
- 22
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The Correct Option is C
Solution and Explanation
The problem involves calculating how many motorcycles would reach B if the cyclist doubled his speed. Let's break down the solution:
- The cyclist takes 1 hour to travel from A to B at his original speed. Therefore, the cyclist would take half an hour (30 minutes) if his speed is doubled.
- From 10:01 am onwards, motorcycles leave A for B every minute.
- Let's calculate how many motorcycles would have left by the time the cyclist reaches B in 30 minutes, i.e., by 10:30 am.
- Between 10:01 am and 10:30 am, the motorcycles leave each minute. Hence, a total of 30 minutes pass in this window.
- Thus, 30 motorcycles leave from 10:01 am to 10:30 am.
- However, the problem states that 45 motorcycles reach B by 11 am when the cyclist originally took 1 hour. Doubling the cyclist's speed means calculating motorcycles that reach by 10:30 am when the cyclist doubles his speed.
- Since it takes the motorcycles 1 hour to reach B (from 10:01 am to 11:00 am originally), the 30 motorcycles that left between 10:01 am to 10:30 am will just be reaching B by 11 am. Halfway through, for 30 minutes, no motorcycles would reach B because they still need a full hour to reach it.
- Therefore, only those motorcycles that left in the previous cycle, i.e., from 10:31 am up to 11:00 am minus 15 motorcycles (since 15 motorcycles would arrive between 10:30 am to 11:00 am), would have reached earlier by 11:00 am.
- Thus, 45 - 30 = 15 motorcycles would have reached by 10:30 am when the cyclist's speed is doubled.
The correct answer is: 15
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