Quantitative Ability - Question of the Day

QUESTION:-

A tank has two taps to empty it. Time taken to empty the tank when only tap A is opened is 6 hours, while it is 10 hours when only tap B is opened. When both the taps are opened together, a design fault causes 20 litres of water to be emptied less per hour than the expected rate, and so the tank gets emptied in 6 hours. What is the capacity of the tank in liters?

OPTIONS

1) 80
2) 180
3) 120
4) 200

Solution
Let the capacity of the tank be X liters.
Since both the taps individually take 6 and 10 hours respectively to empty the tank, time taken to empty the tank when both the taps are opened should be

Thus, the fraction of tank expected to be emptied per hour is  4/15 .

Now, due to a design fault, 20 litres of water per hour gets emptied less.
∴ Amount of water that flows out of the tank every hour

Since the capacity of tank is X liters, 4X/15liters are expected to flow out of tank every hour.

∴ Time taken to empty the tank with capacity of x litres
∴ 15x = 24x – 1800
∴ 9x = 1800
∴ x = 200 litres
Hence, option 4.