Two friends A and B are running up hill and then to get down! length of road is 440 yards. A on his return journey met B going up at 20 yards from top, A has finished the race 5 minutes earlier than B, then how much time A had taken to complete the race.  Choose the correct choice from the following options:
A) 50 minutes  B) 52.5 minutes  C) 55 minutes  D) 54.5 minutes  E) None of these
Explanation :   When A travels 460m (=440+20),   B travels 420m (=440-20). So, ratio of speed = 460:420   = 23:21.   Let A's speed be 23x, and that of B's be 21x.   =&gt; 23x = ((2 * 440) / t) which implies 23t = 880/x;   =&gt; 21x = ((2 * 440) / (t+5)) which implies 21(t+5) = 880/x.   From these two equations, 23t = 21(t+5). Solving, t = 52.5   Hence (B) is the correct answer.   Answer : 52.5 minutes
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Two friends A and B are running up hill and then to get down! length of road is 440 yards. A on his return journey met B going up at 20 yards from top, A has finished the race 5 minutes earlier than B, then how much time A had taken to complete the race.