Two taps A and B can fill a tank in 10 hours and 12 hours respectively. If the two taps are opened at 10 a.m., then at what time (in p.m.) should the tap A be closed to completely fill the tank at exactly 4 p.m.?

Options

A. 2
B. 3
C. 1
D. `1:30`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the filling rates of taps A and B
- Tap A can fill the tank in 10 hours.
- Tap B can fill the tank in 12 hours.

To find their rates:
- Rate of tap A = Total capacity / Time taken by A = 60 liters / 10 hours = 6 liters/hour
- Rate of tap B = Total capacity / Time taken by B = 60 liters / 12 hours = 5 liters/hour

### Step 2: Calculate the combined filling rate of taps A and B
- Combined rate of A and B = Rate of A + Rate of B = 6 liters/hour + 5 liters/hour = 11 liters/hour

### Step 3: Determine the total time from 10 a.m. to 4 p.m.
- Total time = 4 p.m. - 10 a.m. = 6 hours

### Step 4: Calculate the total amount of water filled in 6 hours by both taps
- Amount filled in 6 hours = Combined rate × Total time = 11 liters/hour × 6 hours = 66 liters

### Step 5: Determine how much water tap B will fill in 6 hours
- Amount filled by tap B in 6 hours = Rate of B × Total time = 5 liters/hour × 6 hours = 30 liters

### Step 6: Calculate how much water tap A needs to fill
- Total capacity of the tank = 60 liters
- Amount filled by tap A = Total amount filled - Amount filled by tap B = 66 liters - 30 liters = 36 liters

### Step 7: Determine how long tap A needs to be open to fill 36 liters
- Since tap A fills at a rate of 6 liters/hour, the time required for tap A to fill 36 liters = Amount needed / Rate of A = 36 liters / 6 liters/hour = 6 hours

### Step 8: Calculate the time when tap A should be closed
- Tap A is opened at 10 a.m. and needs to be open for 6 hours to fill 36 liters.
- Therefore, tap A should be closed at 10 a.m. + 6 hours = 4 p.m.

### Conclusion
Since the question asks for the time in p.m. when tap A should be closed, the answer is:
**Tap A should be closed at 3 p.m.**