A9 PM
B9.45 PM
C9.30 PM
D10 PM
Answer:
D. 10 PM
Read Explanation:
Pipe A fills the tank in 9 hours. This means in 1 hour, Pipe A fills 1/9 of the tank.
Pipe B fills the tank in 12 hours. This means in 1 hour, Pipe B fills 1/12 of the tank.
Pipe C empties the tank in 18 hours. This means in 1 hour, Pipe C empties 1/18 of the tank.
The combined efficiency of pipes A and B (filling) is the sum of their individual efficiencies: 1/9 + 1/12.
To add these fractions, find a common denominator, which is 36. So, (4/36) + (3/36) = 7/36 of the tank filled per hour by A and B together.
When Pipe C is also open (emptying), the net efficiency is the combined filling efficiency minus the emptying efficiency: 7/36 - 1/18.
The common denominator is 36. So, (7/36) - (2/36) = 5/36 of the tank filled per hour when all three pipes are working.
From 3 PM to 4 PM: Only Pipe A is working. It fills 1/9 of the tank.
From 4 PM to 5 PM: Pipes A and B are working. In this hour, they fill an additional 1/9 + 1/12 = 7/36 of the tank.
Total filled by 5 PM: The total portion of the tank filled by 5 PM is the sum of work done in the first two hours: 1/9 + 7/36 = 4/36 + 7/36 = 11/36.
Remaining work: The fraction of the tank yet to be filled is 1 - 11/36 = 25/36.
From 5 PM onwards, all three pipes (A, B, and C) are operational.
Their combined net efficiency is 5/36 of the tank per hour.
To find the time required to fill the remaining 25/36 of the tank, divide the remaining work by the net efficiency: (25/36) / (5/36).
This simplifies to 25/5 = 5 hours.
Since all three pipes start working effectively from 5 PM, and it takes 5 more hours to fill the remaining tank, the tank will be filled 5 hours after 5 PM.
Therefore, the tank will be filled at 10 PM.