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