Together, the three intake pipes, "P," "Q," and "R," can fill a water tank in eight hours. While the three pipes are opened simultaneously, pipe "Q" closes after three hours. Determine how long pipe "Q" took to fill the same tank by itself if pipes "P" and "R" completed the remaining portion in 9 hours.

Solution

ATQ, Let quantity filled by pipe ‘P’, ‘Q’ and ‘R’ together in 8 hrs = 1 litres Quantity filled by pipe ‘P’, ‘Q’ and ‘R’ together in 1 hrs = (1/8) litres Quantity filled by pipe ‘P’, ‘Q’ and ‘R’ together in 3 hrs = (3/8) litres Remaining quantity to be filled = {1 – (3/8)} = (5/8) litres Quantity filled by pipe ‘P’ and ‘R’ together in 9 hrs = (5/8) litres Quantity filled by pipe ‘P’ and ‘R’ together in 1 hrs = (5/72) litres Quantity filled by pipe ‘Q’ alone in 1 hour = (1/8) – (5/72) = (4/72) litres So, pipe ‘Q’ alone can fill the tank in (72/4) = 18 hrs