Question 94

Two pies A and B can separately fill a cistern in 60 min and 75 min respectively.. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 min In how much time the third pipe alone can empty the cistern ?

Solution

Let the volume of the cistern be 300 units

Rate at which A fills the cistern = $$\frac{300}{60}$$ = 5 units/min

Rate at which B fills the cistern = $$\frac{300}{75}$$ = 4 units/min

Let rate at which third pipe em[ties it = $$x$$ units/min

Acc to ques :

=> $$(5 + 4 - x) * 50 = 300$$

=> $$9 - x = 6$$

=> $$x = 3$$

$$\therefore$$ Time taken by third pipe alone to empty the tank = $$\frac{300}{3}$$ = 100 min

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