Question

There are two pipes leading to a tank. If pipe X alone is opened, the tank will be filled in 20 minutes. If pipe Y alone is opened, the tank will be filled in 25 minutes. Both pipes were opened together. After 5 minutes, pipe Y was closed. How long should pipe Y be left open to fill the rest of the tank?

• A. 10 minutes
• B. 15 minutes
• C. 12.5 minutes
• D. 11 minutes

Answer 1

Answer:

D. 11 minutes

• Pipe X fills the tank in 20 minutes. Therefore, in 1 minute, Pipe X fills 1/20 of the tank. This is its filling rate.

• Pipe Y fills the tank in 25 minutes. Therefore, in 1 minute, Pipe Y fills 1/25 of the tank. This is its filling rate.

• When both pipes are opened together, their filling rates add up.

• Combined rate = Rate of Pipe X + Rate of Pipe Y

• Combined rate = 1/20 + 1/25

• To add these fractions, find a common denominator, which is 100.

• Combined rate = 5/100 + 4/100 = 9/100 of the tank per minute.

Work Done in the First 5 Minutes

• Both pipes were opened together for 5 minutes.

• In 5 minutes, the portion of the tank filled is: Combined Rate × Time

• Portion filled = (9/100) × 5 = 45/100 or 9/20 of the tank.

Remaining Work

• The total capacity of the tank is considered as 1 (or 100%).

• Remaining portion of the tank to be filled = Total Capacity - Portion Filled

• Remaining portion = 1 - 9/20 = 11/20 of the tank.

Time Taken by Pipe X to Fill the Remaining Tank

• After 5 minutes, Pipe Y was closed. Only Pipe X is working.

• Pipe X fills 1/20 of the tank per minute.

• Time taken by Pipe X to fill the remaining 11/20 of the tank = Remaining Portion / Rate of Pipe X

• Time = (11/20) / (1/20)

• Time = (11/20) × (20/1) = 11 minutes.