In a 100 m race, if X gives Y a start of 25 m, then X wins the race by 5 second. Alternatively, if X gives Y a start of 50 m the race ends…

We know that, speed = distance/time taken

Given: In a 100 m race, if X gives Y a start of 25 m, then X wins the race by 5 second and if X gives Y a start of 50 m the race ends in a dead heat, then

In the first case:

Distance for X = 100m

Distance for Y = 75 m

If time taken by X be t sec., then that for Y will be (t + 5) seconds.

Thus, speed of X, s1’ = 100/t m/sec and that for Y, s2’ = 75/(t + 5) m/sec ---------(i)

Now, in the second case:

Distance for X = 100 m

Distance for Y = 50 m

Since time taken by X be t sec, then that for Y will also be t sec.

Thus, speed of Y, s2’’ = 50/t m/sec

Since s2’ = s2’’. Thus,

$(\frac{{75}}{{t + 5}} = \frac{{50}}{t})$

⇒ 75t = 50t + 250

⇒ 25t = 250

⇒ t = 10 sec.

∴ Speed of X = 100/10 = 10m/sec

∴ time-taken by X to run 200 m = (200/10) sec

= 20 sec