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Pipe P alone takes 15 hours to fill the tank and pipe Q alone takes 12 hours to fill the tank. Pipe R alone takes 20 hours to empty the tank. The tank is already 1/4th filled then all three pipes are opened together. How much it will take to fill the remaining portion of the tank by all three pipes?

Pipe P alone takes 15 hours to fill the tank and pipe Q alone takes 12 hours to fill the tank. Pipe R alone takes 20 hours to empty the tank. The tank is already 1/4th filled then all three pipes are opened together. How much it will take to fill the remaining portion of the tank by all three pipes? Correct Answer 7.5 hours

Given,

Pipe P's 1 hour's work = 1/15

Pipe Q's 1 hour's work = 1/12

Pipe R's 1 hour's work = 1/20

Pipe (P + Q + R)’s 1 hour's work = 1/15 + 1/12 – 1/20 = 1/10

Remaining portion of tank = 1 – 1/4 = 3/4

Time taken by three pipes to fill 3/4th of tank =

= 3/4 × 10 = 15/2

It will take 15/2 = 7.5 hours to fill 3/4th tank.

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