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Pipes P and Q alone can fill a tank in 15 hours and 20 hours respectively. An inlet pipe R is 25% more efficient than pipe P and an outlet pipe S is 16(2/3)% less efficient than pipe Q. Pipe P and pipe S are opened together. If after 1 hour pipe Q is opened and after 1 more hour pipe R is opened, then in what time the tank will be filled ?

Pipes P and Q alone can fill a tank in 15 hours and 20 hours respectively. An inlet pipe R is 25% more efficient than pipe P and an outlet pipe S is 16(2/3)% less efficient than pipe Q. Pipe P and pipe S are opened together. If after 1 hour pipe Q is opened and after 1 more hour pipe R is opened, then in what time the tank will be filled ? Correct Answer 7(13/19) hours

The time taken by pipe P alone to fill the tank = 15 hours

The time taken by pipe Q alone to fill the tank = 20 hours

The time taken by pipe R alone to fill the tank = 15 × 100/125 = 12 hours

The time taken by pipe S alone to empty the tank = 20 × 300/250 = 24 hours

Suppose the capacity of the tank = LCM of 15, 20, 12 and 24 = 120 units

The quantity of tank filled by pipe P alone in 1 hour = 120/15 = 8 units

The quantity of tank filled by pipe Q alone in 1 hour = 120/20 = 6 units

The quantity of tank filled by pipe R alone in 1 hour = 120/12 = 10 units

The quantity of tank emptied by pipe S alone in 1 hour = 120/24 = 5 units

According to the question:

In the first 1 hour the quantity of tank filled by pipes P and S together = 8 – 5 = 3 units

In next 1 hour the quantity of tank filled by pipes P, Q and S together = 8 + 6 – 5 = 9 units

Remaining quantity to be filled = 120 – 3 – 9 = 108 units

Now, all the 4 pipes are opened:

So, the total time taken to fill the tank = 2 + = 7(13/19) hours

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