In a race of length X metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N)
Choose the most appropriate option:
A) X(X-N) / X-M
B) X(N-M) / X-M
C) X-N
D) M-N
E) M+N
As the time is constant, the ratio of distances will be the same as the ratio of speeds.   If Sj,Sl,Sg are the speeds of Johnson, Lewis, and Greene respectively, then   Sj/Sl = X/(X-M)   and Sj/Sg = X/(X-N)   =&gt; Sg/Sl = (X-N)/(X-M)   Therefore the speeds of Lewis and Greene are in the ratio (X-M)/(X-N)   When Lewis finishes the race, the time run by him and Greene are same   =&gt; The ratio of the speeds of Lewis and Greene will be the same as the ratio of distances run by them.   =&gt; Distance run by Greene when Lewis finishes the race = (X-N)/(X-M) * X   =&gt; Lewis beats Greene by X- X*(X-N)/(X-M) = X [ 1 - (X-N)/(X-M)] = X (N-M) / (X-M)   Option (X(N-M) / X-M) is therefore correct.
<result>B</result>
In a race of length X metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N)