Pipes A and B can fill a tank in 6 hours and 8 hours, respectively. Both pipes are opened together for 3 hours. After that pipe A is closed, and B continues to fill the tank. In how many hours will the tank be filled?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 4.
⇒ Pipe A can fill the tank in 6 hours, so its rate is 1/6 of the tank per hour.
⇒ Pipe B can fill the tank in 8 hours, so its rate is 1/8 of the tank per hour.
Calculate the combined rate of both pipes:
⇒ Combined rate = Pipe A's rate + Pipe B's rate = 1/6 + 1/8 = 7/24 of the tank per hour.
Calculate the portion of the tank filled in the first 3 hours:
⇒ Portion filled in 3 hours = Combined rate × time = (7/24) × 3 = 7/8 of the tank.
Calculate the remaining portion of the tank to be filled:
⇒ Remaining portion = 1 - Portion filled = 1 - 7/8 = 1/8 of the tank.
Calculate the time taken by pipe B to fill the remaining portion:
⇒ Time taken by B = Remaining portion ÷ Pipe B's rate = (1/8) ÷ (1/8) = 1 hour.
Calculate the total time taken to fill the tank:
⇒ Total time = Time both pipes were open + Time taken by B alone = 3 + 1 = 4 hours.
Therefore, the tank will be filled in a total of 4 hours.