Question: In a race of length D m , A beats B by X m and C by Y m. By what distance does B beat C in the same race?

A: (Y-X)D / (D-Y) m
B: (Y-X)D / (D-X) m
C: (D-Y)D / (D-X) m
D: (D-X)D / (D-Y) m

Ans: B
Solution: Suppose time taken by A, B and C  to finish the race are t1, t2, t3 respectively.
So Speed of A, B and C are D/t1, D/t2 and D/t3
Now When A finishes the race distance travelled by B = Dt2/t1
                                        and  distance travelled by C = Dt3/t1
According to question, D-Dt2/t1 = X   ............(i)
                             and D-Dt3/t1 = Y   ............(ii)

We have to find D-Dt3/t2
from (i)  t2/t1 = (D-X)/D ..... (iii)
from (ii) t3/t1 = (D-Y)/D ..... (iv)
From (iii) and (i) we get t3/t2 = (D-Y)/(D-X)

So, D-Dt3/t2
= D[(1-(D-Y)/(D-X)]
= D(Y-X)/(D-X)
Hence B