Question
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)? Â (1) 12Â Â Â Â Â (2) 15Â Â Â Â Â (3) 22Â Â Â Â (4) 25Â Â Â ÂSolution
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.
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