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 60 % of the length of the race ?
"first calculate the distance , b has covered with his speed in the time , in which a reached 40 % 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 ( 0.4 ) = 0.26 ( which means b would have covered 0.26 of the race length during the time in which a has covered 0.4 of the race length . therefore to win , b needs a headstart of ( 1 - 0.26 = ) 0.74 of the race length . so the answer is e"
multiply(subtract(const_1, multiply(divide(subtract(const_100, 60), const_100), divide(13, 20))), const_100)