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)? (1) 12 (2) 15 (3) 22 (4) 25Solution
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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