How much of a start should Bhavesh give to Chetan so they would finish the race at the same time?

Question

There are three runners Ahaan, Bhavesh, and Chetan.
Each runs with a different uniform speed in a 1000 meters race.

If Ahaan gives Bhavesh a start of 50 meters, they will finish the race at the same time.

If Ahaan gives Chetan a start of 69 meters, they will finish the race at the same time.

Suppose Bhavesh and Chetan are in a race.
How much of a start should Bhavesh give to Chetan so they would finish the race at the same time?

Answer 1

20 m

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Speed of Ahaan=a
Speed of Bhavesh=b
Speed of Chetan=c
We know a>b>c
time they spent = t=1000/a=(1000-50)/b=(1000-69)/c --> 1000/a=950/b=931/c
We have 950/b=931/c and we need to find out 1000/b=x/c, x will be the distance Chetan can run at the same time
To do that we multipy both sides to 1000/950 --> 1000/950*950/b=1000/950*931/c--> 1000/b=980/c
1000-980=20 m is the answer