Question 17

# Two pipes A and B can fill a cistern in 120 minutes and 150 minutes respectively. There is also an outlet C.If all the three pipes are opened together, the cistern gets filled in 100 minutes. How much time will be taken by C to empty full tank?

Solution

Let the capacity of the cistern be 600 units.

From the given data, the efficiencies of pipes A and B are 5 units/ min and 4 units/min respectively.

Let the efficiency of outlet pipe C be 'k' units/min.

Given the time taken to fill the cistern when all the three pipes are open = 100 minutes

$$\Rightarrow Efficiency of pipes\times time taken = Capacity of cistern$$.

$$\Rightarrow (5+4-k)\times 100 = 600$$

$$\Rightarrow 9-k = 6$$

$$\Rightarrow k = 3$$

Therefore the time taken(t)  by pipe C to empty the cistern = $$Capacity of the cistern\div efficiency of pipe C$$

$$\Rightarrow t = 600\div 3 = 200 minutes = 3 hrs 20 min$$.

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