Question 108

Three pipes A, B and C are connected to a tank. Out of the tree, A and B are tile inlet pipes and C is the outlet pipe If opened separately, A fills the tank in 10 hours and B fills the tank in 30 hours. If all three are opened simultaneously, it takes 30 minutes extra than if only A and B are opened. How much time does it take to empty the tank if only C is opened?

We will assume the capacity of the tank to be 30 litres i.e. LCM of 10 and 30.
Efficiencies of Pipe A and B are 3 and 1 litres per hour respectively.
Together they can fill the tank in $$\frac{30}{3+1}=7.5\ hrs$$.
But, when they all work together, they can fill the tank in 30 mins + 7.5 hrs = 8 hrs.
Let us assume the efficiency of C to be X litres per hour. 
So, when they all work together, 8*(3 + 1 - X) = 30
X = 1/4 litres/ hour.
So, time taken by C alone = $$\frac{30}{\frac{1}{4}}=120\ hrs$$.

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