The ratio of time taken by pipes P, Q and R to fill a tank alone is 4 : 6 : 12, respectively. If all three pipes are opened together, the tank is completely filled in 18 hours. Find the time taken by pipe Q alone to fill 7/9 of the same tank.

ATQ, Let the time taken by pipes P, Q and R alone be 4x, 6x and 12x hours. Work done by pipe P in 1 hour = 1/4x Work done by pipe Q in 1 hour = 1/6x Work done by pipe R in 1 hour = 1/12x Work done by all three pipes in 1 hour = 1/4x + 1/6x + 1/12x LCM of 4, 6 and 12 = 12 So, work done in 1 hour = (3 + 2 + 1)/12x Work done in 1 hour = 6/12x Work done in 1 hour = 1/2x Time taken by all three pipes together to fill the tank = 1 ÷ (1/2x) Time taken = 2x According to the question: 2x = 18 x = 18/2 x = 9 Time taken by pipe Q alone to fill the full tank = 6x Time taken by pipe Q alone = 6 × 9 = 54 hours Time taken by pipe Q alone to fill 7/9 of the tank = 54 × 7/9 Time taken = 6 × 7 = 42 hours