Question
There are two inlet pipes 'A', 'B' and one outlet pipe 'C'
in a tank. ‘A’ and ‘B’ can fill the tank in 24 minutes and 16 minutes respectively. ‘C’ is 50% less efficient than ‘A’. If ‘A’ and ‘C’ are open together but after 12 minutes ‘A’ is replaced with ‘B’, then find the total time required to fill the tank completely.Solution
Let the total capacity of the tank be 48x units (LCM of 24 and 16).
Efficiency of A = 48x / 24 = 2x units/min
Efficiency of B = 48x / 16 = 3x units/min
Efficiency of C = 50% of 2x = 1x units/min
Tank filled in first 12 minutes = (2x - 1x) × 12 = 12x units
Remaining = 48x - 12x = 36x units
Time = 36x / (3x - 1x) = 36x / 2x = 18 minutes
Total time = 12 + 18 = 30 minutes
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