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A pipe takes 12 minutes extra to fill a tank due to leakage at the bottom of the pipe. The leakage is 1/4th of its inflow. The inflow can fill the tank in how many minutes?

A pipe takes 12 minutes extra to fill a tank due to leakage at the bottom of the pipe. The leakage is 1/4th of its inflow. The inflow can fill the tank in how many minutes? Correct Answer 36 minutes

GIVEN:

(i) Due to leakage, the tap takes 12 minutes extra to fill the tank.

(ii) Leakage is 1/4th in size of inflow.

CONCEPT:

(i) Leakage is nothing but a separate tap that is at the bottom of a tank.

(ii) Tap filling the tank is doing positive work. Their timing will also be denoted by a positive number.

(iii) Tap emptying the tank is doing negative work. Their timing will also be denoted as a negative numbers.

(iv)Time to fill the tank ∝ (1/Area of a pipe)

FORMULA USED:

(i) Total work = 1-day work × Time to complete the full work.

CALCULATION:

Let, the inflow be tap A and leakage be tap B.

= 3/4

⇒ Timing ratio = 4/3

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⇒ 1 unit = 12 minutes,

⇒ 3 units = 36 minutes, A(inlet flow) can fill the tank in 36 minutes

⇒ 4 units = 48 minutes, (A + B)(inlet + outlet) can fill the tank in 48 minutes.

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