Question 24

Two pipes P and Q can fill a tank in 20hrs and 25hrs respectively while a third pipe R can empty the tank in 30hrs. If all the pipes are opened together for 10hrs and then pipe R is closed then in what time the tank can be filled.

Solution

Let, the volume of the tank be 1500 liters

So, efficiency of pipe P = $$\dfrac{1500}{20}=75$$ liters/ hour.

Efficiency of pipe Q = $$\dfrac{1500}{25}=60$$ liters/ hour.

and, efficiency of pipe R = $$-\dfrac{1500}{30}=-50$$ liters/ hour.

(Since, pipe R is emptying)

So, when all the pipes work together, volume of the tank filled by them = $$\left(75+60-50\right)\times\ 10$$ liters = $$850$$ liters

Now, volume of the tank, that is required to be filled = $$1500-850\ =\ 650$$ liters

And, this has to be filled by pipe P and Q

So, time required to fill the remaining part = $$\dfrac{650}{75+60}=\dfrac{650}{135}=\dfrac{130}{27}$$ hours

So, total time = $$\dfrac{130}{27}+10=\dfrac{400}{27}$$ hours

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