Question
An empty tank can be filled by an inlet pipe in 10
hours, while an outlet pipe can empty it in 15 hours. If we open (N - 1) outlet pipes of the same capacity and (N + 1) inlet pipes also of the same capacity, the tank is filled in 3 hours. Determine the number of inlet pipes used.Solution
Let the capacity of tank be 30 litres (LCM of 10 and 15) Efficiency of 1 inlet pipe = (30/10) = 3 units/litre Efficiency of 1 outlet pipe = (30/15) = 2 units/litre ATQ, {3 X (N + 1) - 2 X (N - 1) } X 3 = 30 Or, (3N + 3 - 2N + 2) X 3 = 30 Or, N + 5 = 10 So, 'N' = 5 Required number of inlet pipes used = (n + 1) = 5 + 1 = 6
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