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Two taps can fill a tank individually in 10 min and 20 min respectively without any leakage. However, there is a leakage at the bottom which can empty the filled tank in 40 min. In how much time will both the taps fill the tank with leakage?

Two taps can fill a tank individually in 10 min and 20 min respectively without any leakage. However, there is a leakage at the bottom which can empty the filled tank in 40 min. In how much time will both the taps fill the tank with leakage? Correct Answer 8 minutes

Given - 

Two taps A and B fill the tank individually in 10 min and 20 min respectively.

A leakage C at the bottom which can empty it in 40 min.

Solution - 

Let the capacity of the tank = LCM of (10, 20, 40) = 40 unit

⇒ Efficiency of A = 40/10 = 4 unit/min

⇒ Efficiency of B = 40/20 = 2 unit/min

⇒ Efficiency of C = 40/40 = 1 unit/min

⇒ (A + B - C) = (4 + 2 - 1) unit/min = 5 unit/min

⇒ time = 40/5 = 8 min

∴ time taken by Both the taps fill the tank with leakage is 8 min.

 

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