A's speed is 20/13 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 80% of the length of the race?
Choose the correct answer.
A) 44 %
B) 48 %
C) 52 %
D) 42 %
E) 87 %

Rationale: "first calculate the distance , b has covered with his speed in the time , in which a reached 20 % 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 20 / 13 of b , therefore , b ' s speed is 13 / 20 of a distance covered by b = speed x time = ( 13 / 20 ) x ( 0.2 ) = 0.13 % ( which means b would have covered 0.13 of the race length during the time in which a has covered 0.2 of the race length . therefore to win , b needs a headstart of ( 1 - 0.13 = ) 0.87 of the race length . so the answer is e"
Answer: E