In a race of length L metres, Johnson beats Lewis by Y metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (Y<N) Pick.
A) L(L-N) / L-Y  B) L(N-Y) / L-Y  C) L-N  D) Y-N  E) Y+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 = L/(L-Y)   and Sj/Sg = L/(L-N)   =&gt; Sg/Sl = (L-N)/(L-Y)   Therefore the speeds of Lewis and Greene are in the ratio (L-Y)/(L-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 = (L-N)/(L-Y) * L   =&gt; Lewis beats Greene by L - L*(L-N)/(L-Y) = L [ 1 - (L-N)/(L-Y)] = L (N-Y) / (L-Y)   Option (L(N-Y) / L-Y) is therefore correct.
<result>B</result>
In a race of length L metres, Johnson beats Lewis by Y metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (Y<N)