Question

The length of a circular track is 800 m. Virat and Amresh started from the same point on the track and ran in opposite directions. Virat took 12 minutes to cover one kilometer while Amresh took only 9 minutes to cover the same distance. They kept running for 90 minutes. How many times did they cross each other?

Answer 1

Given:

The length of a circular track is 800 m.

Virat and Amresh started from the same point on the track and ran in opposite directions.

Virat took 12 minutes to cover one kilometer while Amresh took only 9 minutes to cover the same distance.

They kept running for 90 minutes.

To find:

How many times did they cross each other?

Solution:

The time taken to cover one kilometer for Virat and Amresh is in the ratio

4 : 3

Their speeds are in the ratio 3 : 4.

Virat covers 3/7th of the track and Amresh covers 4/7th from one crossing to the next i.e.

Virat covers 3/7 × 800 m from one crossing to the next.

In 90 min, Virat covers  90/12 × (1000) = 7500 m.  

The number of crossings  

$=\dfrac{7500 \times \frac{7}{3}}{800}$

$=\dfrac{175}{8}$

= 21.87

So, Virat and Amresh will meet 21 times.