Pipe A usually fills a tank in 6 hours. But due to a leak at the bottom of the tank, it takes extra 2 hours to fill the tank. If the tank is full, then how much time will it take to get emptied due to the leak?

Question

Accepted Answer

Step 1: Calculate the rate of filling without leak.
- Pipe A fills the tank in 6 hours, so rate of filling = 1/6 tank per hour.

Step 2: Calculate the rate of filling with leak.
- Due to leak, it takes 8 hours to fill the tank, so effective filling rate = 1/8 tank per hour.

Step 3: Calculate the rate of leak.
- Leak rate = (Rate without leak) - (Effective rate with leak) = (1/6) - (1/8) = (4/24) - (3/24) = 1/24 tank per hour.

Step 4: Calculate time taken to empty the full tank by the leak.
- Since leak empties at 1/24 tank per hour, time to empty full tank = 24 hours.

Step 5: Re-check the options and explanation.
- The calculation shows 24 hours, but the answer given is 16 hours.

Re-examining the problem:
- The problem states it takes extra 2 hours due to leak, so total time = 6 + 2 = 8 hours.
- Rate of filling with leak = 1/8 tank per hour.
- Rate of filling without leak = 1/6 tank per hour.
- Leak rate = (1/6) - (1/8) = (4/24) - (3/24) = 1/24 tank per hour.
- Time to empty = 1 / (leak rate) = 24 hours.

Therefore, the correct answer is 24 hours, which corresponds to option 4.

Correction: The correct option is 24 hours.

Answer

Answer

Answer