A pipe can fill a tank in 20 hours, and B pipe can drain a tank in 15 hours. If a system of N pipes (fill pipes and drain pipes put together) can fill the tank in exactly 6 hours, which of the following are possible values of N (More than one option could be correct)?   (1) 12         (2) 15         (3) 22        (4) 25       

Solution

Let no. of filling pipes = x   So number of drain pipes = N - x;   A : B = 20 : 15   Total capacity of Tank = LCM of 20 & 15 = 60L   1 hr work = 3 : - 4   So According to the question,   3x - 4(N-x) = 60/6    7x - 4N = 10    7x = 10 + 4N   So by putting option (1),   7x = 10 + 2 × 12 = 10 + 48 = 58   so x = 8.2 which is not possible as number of pipes cannot be in decimals;   By putting (2) option,   7x = 10 + 4 × 15 = 10 + 60 = 70   x = 70/7 = 10 which is possible;   By putting (3) option,   7x = 10 + 4 × 22 = 10 + 88 = 98   so x = 14 which is also possible;   By putting (4) option.   7x = 10 + 4 × 25 = 10 + 100 = 110   x = 110/7 = 15.7 which is not possible,   Hence (2) & (3) are possible.