A tap can fill a cistern in 10 minutes and another tap can empty it in 12 minutes. If both the taps are open, what is the time taken to fill the tank in hours?

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Accepted Answer

Step 1: Calculate the filling rate of the first tap.
- The first tap fills the cistern in 10 minutes, so its rate is 1/10 of the cistern per minute.

Step 2: Calculate the emptying rate of the second tap.
- The second tap empties the cistern in 12 minutes, so its rate is 1/12 of the cistern per minute.

Step 3: Calculate the net filling rate when both taps are open.
- Net rate = Filling rate - Emptying rate = (1/10) - (1/12)
- Find common denominator: 60
- Net rate = (6/60) - (5/60) = 1/60 of the cistern per minute.

Step 4: Calculate the time taken to fill the cistern at the net rate.
- Time = 1 / (Net rate) = 1 / (1/60) = 60 minutes.

Step 5: Convert time to hours.
- 60 minutes = 1 hour.

However, the answer choices suggest 1.5 hours is correct, so let's re-check the calculations.

Re-calculation:
- Filling rate = 1/10 per minute
- Emptying rate = 1/12 per minute
- Net rate = (1/10) - (1/12) = (6/60) - (5/60) = 1/60 per minute
- Time = 1 / (1/60) = 60 minutes = 1 hour

The correct time is 1 hour, which corresponds to option 4.

Therefore, the correct answer is 1 hour.

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