Pipe X can fill a tank in 9 hours and Pipe Y can fill it in 21 hours. If they are opened on alternate hours and Pipe X is opened first, in how many hours shall the tank be full?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. .
Time required for pipe X to fill the tank = 9 hours
Time required for pipe Y to fill the tank = 21 hours
In the first hour, Pipe X fills 1/9 of the tank and Pipe Y fills 1/21 in the second hour.
In two hours, both Pipe X and Pipe Y fill = (1/9) + (1/21) = 10/63 of the tank
Pipe X and Pipe Y fill in 12 hours = (10/63) × 6 = 20/21 of the tank
Remaining quantity = 1 - (20/21) = 1/21
Time required for Pipe X to fill 1/21 part = (1/21)/(1/9) = 3/7 hours
Total time = 12 + (3/7) = hours
Therefore, the tank shall be full in hours.