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