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MAT Exam 2020 Paper

Question : 115 of 200

Marks: +1, -0

A

and

B

walk around a circular track. They start at 8 am from the same point in the opposite directions.

A

and

B

walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9:30 am?

Validate

Solution:

Concept:

When two people move in opposite directions around a circular track, their relative speed is the sum of their speeds. Each crossing occurs when their combined distance equals one full round of the track.

Explanation:

Speed of A

= 2\ \text{rounds/hour}

Speed of B

= 3\ \text{rounds/hour}

Since they walk in opposite directions:

Relative speed

= 2 + 3 = 5\ \text{rounds/hour}

Time taken to meet once

= \dfrac{1}{5}

hour

= \dfrac{60}{5} = 12

minutes.

From 8:00 am to 9:30 am, total time is 90 minutes.

So they meet every 12 minutes: at 8:12, 8:24, 8:36, 8:48, 9:00, 9:12, and 9:24 am.

Thus, before 9:30 am, they cross each other 7 times.

Answer:

Option C:

7

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