Two taps A and B can fill a tank in 5 hours and 20 hours respectively. If both the taps are open then due to a leakage, it took 40 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank? a)28 hrb)16 hrc)22 hrd)32 hrCorrect answer is option 'A'. Can you explain this answer?

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Two taps A and B can fill a tank in 5 hours and 20 hours respectively. If both the taps are open then due to a leakage, it took 40 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank?

a)
28 hr
b)
16 hr
c)
22 hr
d)
32 hr

Correct answer is option 'A'. Can you explain this answer?

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Two taps A and B can fill a tank in 5 hours and 20 hours respectively....

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Two taps A and B can fill a tank in 5 hours and 20 hours respectively....

Solution:

Let the capacity of the tank be 'x' litres.

Let the leakage alone can empty the tank in 'y' hours.

Given that, tap A can fill the tank in 5 hours.

So, the rate of tap A = x/5 litres per hour.

Given that, tap B can fill the tank in 20 hours.

So, the rate of tap B = x/20 litres per hour.

Let the leakage rate be 'm' litres per hour.

When both the taps A and B are opened, due to leakage, it took 40 minutes more to fill the tank.

Time taken by taps A and B to fill the tank = (x/(x/5 + x/20 - m)) hours

Time taken by taps A and B to fill the tank in minutes = (x/(x/5 + x/20 - m)) x 60 minutes

Time taken by taps A and B to fill the tank in minutes = (60x/((4x + x - 20m))) minutes

Given that, the time taken to fill the tank with leakage = (60x/((4x + x - 20m))) + 40 minutes

So, (60x/((4x + x - 20m))) + 40 = (x/5 + x/20) x 60

On solving the above equation, we get m = x/140 litres per hour.

Therefore, the leakage alone can empty the tank in 140 hours.

Hence, the correct option is (A) 28 hours.

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