Question 6

# Two inlet pipes can fill a cistern in 20 and 24 hours respectively and an outlet pipe can empty 160 gallons of water per hour. All the three pipes working together can fill the empty cistern in 40 hours. What is the capacity (in gallons) of the tank?

Solution

Let capacity of tank = L.C.M.(20,24,40) = $$120x$$ gallons

1st inlet pipe can fill in 20 hours, => 1st pipe's efficiency = $$\frac{120x}{20}=6x$$ gallons/hr

Similarly, 2nd pipe's efficiency = $$\frac{120x}{24}=5x$$ gallons/hr

Also, efficiency of 3rd outlet pipe = $$-160$$ gallons/hr

According to ques,

=> $$(6x+5x-160)\times40=120x$$

=> $$11x-160=\frac{120x}{40}=3x$$

=> $$11x-3x=160$$

=> $$x=\frac{160}{8}=20$$

$$\therefore$$ Capacity of tank = $$120\times20=2400$$ gallons

=> Ans - (B)