Sam's speed = x
John's speed = y

In an unfair race:
100/x = 84/y
y = 21x/25 ... Eqn1

In a fair race:
100/y - 100/x = 4
100(y-x)=4xy ... Eqn 2

Substituting equation 1 into equation 2:

100(21x/25 - x) = 4x(21x/25)
100*(4/25)*(25/4)*(1/21) = x
x = 100/21

Time taken by Sam = Distance / Sam's speed = 100/(100/21) = 21 sec.

Choose D.

-BM-

sanju09 wrote:In a 100m race, Sam beats John by 4 seconds. On the contrary, if Sam allowed John to start 16m ahead of Sam, then Sam and John reach the finishing point at the same time. How long does Sam take to run the 100m race?

A. 4 seconds

B. 25 seconds

C. 29 seconds

D. 21 seconds

E. 6.25 seconds

Given that in a 100m race Sam beats John by 4 seconds.

If he gives John a head-start of 16 mts, both will finish the race at the same time. From this we can conclude that if John is not given a head-start, Sam will beat John by 16 mts.

So we can conclude that Sam beats John in a 100mts race by 16 mts or 4 sec.

Hence John takes 4 secs to cover 16 mts.
Thus John takes 25 secs to cover 100mts.
So Sam takes 21 secs to cover 100 mts