A's speed is 15/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that B beats A by 40% of the length of the race?  Select the correct option:
A) 44%  B) 48%  C) 52%  D) 42%  E) 46%
First calculate the distance, B has covered with his speed in the time, in which A reached 60% of the race.   Then Add the remaining distance as head start for B to win the race.   Its best to apply Ratios concept here.   Since A's speed is 15/13 of B, therefore, B's speed is 13/15 of A   Distance covered by B = speed x time = (13/15) x (0.6) = 0.52%   (Which means B would have covered 0.52 of the race length during the time in which A has covered 0.6 of the race length.   Therefore to win, B needs a headstart of (1 - 0.52 = ) 0.48 of the race length.   So the answer is 48%
<result>B</result>
A's speed is 15/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that B beats A by 40% of the length of the race?