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In the bottom of a water tank, there are two drains A and B. If only A is open, it takes 30 minutes to empty a full tank and if only B is open, it takes 20 minutes. If for 10 minutes both drains are open, then B is closed, how much time it takes to empty a full tank?

In the bottom of a water tank, there are two drains A and B. If only A is open, it takes 30 minutes to empty a full tank and if only B is open, it takes 20 minutes. If for 10 minutes both drains are open, then B is closed, how much time it takes to empty a full tank? Correct Answer 15 minutes

Given:

Time taken by A to drain water tank = 30 min

Time taken by B to drain water tank = 20 min

Concept Used:

Total work = Efficiency × Time taken to complete the work

Total work = LCM of both Time 

Calculation:

Let us take LCM for (30, 20) = 60 

Total work = 60 unit

Efficiency of A = 60/30 = 2 unit

Efficiency of B = 60/20 = 3 unit

Efficiency of both A and B = 2 + 3 = 5 unit

Total work = Efficiency × Time taken to complete the work

A and B does work for 10 min 

work done for 10 min = 5 × 10 = 50 unit

Remaining work = 60 - 50 = 10 unit

The remaining 10 unit work is done by A alone so,

Total work = Efficiency × Time taken to complete the work

Time taken by A = 10/2 = 5 mins

Total time taken to empty the tank = Time taken by both A and B + Time taken by A

Total time = 10 + 5 ⇒ 15 mins

∴ 15 mins to empty a full tank

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