Question

Ashwin and Bhaskar are friends, and one day they went to a cricket match as ballboys. That cricket
stadium has two identical circular tracks touching each other denoting boundary lines, and it has a
rectangular track enclosing the two circles. The edges of the rectangle are tangential to the circles.
Ashwin and Bhaskar simultaneously started running, from the point where one of the circular tracks
touches the smaller side of the rectangular track. Ashwin runs along the rectangular track, while
Bhaskar runs along the two circular tracks in a figure of eight. Both of them return to the starting point
at the same time. Approximately, what is the ratio of Ashwin's speed to Bharskar's speed?​
1=X=3
4=X=6
7=X=9
10=X=12
13=X=15

Answer 1

Given : Ashwin and Bhaskar simultaneously started running, from the point where one of the circular tracks

touches the smaller side of the rectangular track. Ashwin runs along the rectangular track, while

Bhaskar runs along the two circular tracks in a figure of eight. Both of them return to the starting point

at the same time.

To Find :  Approximately, what is the ratio of Ashwin's speed to Bhaskar's speed?​

Solution:

Let sat radius of circle = r

then diameter = 2r

Hence rectangular field dimension will be 2r  and 4r

Ashwin runs along the rectangular track,  Hence he runs = 2(2r + 4r)

= 12r

Bhaskar runs along the two circular tracks in a figure of eight. Hence he completes both circle

so Bhasker runs = 2 * 2πr = 4πr

ratio of Ashwin's speed to Bhaskar's speed  = 12r/4πr

= 3/π

= 3 /(22/7)

= 21/22

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