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 25% of the length of the race?  Pick one
A) 35 %  B) 48 %  C) 52 %  D) 42 %  E) 46 %

Rationale: first calculate the distance , b has covered with his speed in the time , in which a reached 80 % 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 ( 0.75 ) = 0.65 % ( which means b would have covered 0.65 of the race length during the time in which a has covered 0.75 of the race length . therefore to win , b needs a headstart of ( 1 - 0.65 = ) 0.35 of the race length . so the answer is a
Answer: A