Pipe A can fill a tank in 6 hours. Pipe B can fill the same tank in 8 hours. Pipe A, B and C together can fill the same tank in 12 hours. Then which of the following statements is true for pipe C?

Options

A. It can fill all the tank in 4 hours 40 minutes
B. It can fill all the tank in 4 hours 48 minutes
C. It can empty the tank in 4 hours 48 minutes
D. It can empty the tank in 4 hours 40 minutes

Answer

To solve the problem, we need to determine the rate at which Pipe C can fill or empty the tank based on the information given about Pipes A and B.

### Step-by-Step Solution:

1. **Determine the rates of Pipe A and Pipe B:**
- Pipe A can fill the tank in 6 hours. Therefore, the rate of Pipe A (A) is:
\[ A = \frac{1}{6} \text{ tanks per hour} \]
- Pipe B can fill the tank in 8 hours. Therefore, the rate of Pipe B (B) is:
\[ B = \frac{1}{8} \text{ tanks per hour} \]

2. **Determine the combined rate of Pipes A, B, and C:**
- Together, Pipes A, B, and C can fill the tank in 12 hours. Therefore, their combined rate is:
\[ A + B + C = \frac{1}{12} \text{ tanks per hour} \]

3. **Set up the equation:**
- We can express the combined rate in terms of the individual rates:
\[ \frac{1}{6} + \frac{1}{8} + C = \frac{1}{12} \]

4. **Solve for C:**
- Rearranging the equation gives:
\[ C = \frac{1}{12} - \frac{1}{6} - \frac{1}{8} \]

5. **Find a common denominator:**
- The least common multiple (LCM) of 6, 8, and 12 is 24. We convert each fraction:
\[ \frac{1}{6} = \frac{4}{24}, \quad \frac{1}{8} = \frac{3}{24}, \quad \frac{1}{12} = \frac{2}{24} \]
- Substitute these values back into the equation:
\[ C = \frac{2}{24} - \frac{4}{24} - \frac{3}{24} \]
- Simplifying gives:
\[ C = \frac{2 - 4 - 3}{24} = \frac{-5}{24} \]

6. **Interpret the result:**
- Since C is negative, it indicates that Pipe C is emptying the tank rather than filling it. To find out how long it takes for Pipe C to empty the tank, we take the reciprocal of the rate:
\[ \text{Time taken by C} = \frac{24}{5} \text{ hours} \]

7. **Convert hours to hours and minutes:**
- Dividing gives:
\[ 24 \div 5 = 4 \text{ hours and } 4 \text{ minutes} \]
- Thus, the time taken to empty the tank is 4 hours and 48 minutes.

### Conclusion:
Pipe C can empty the tank in **4 hours and 48 minutes**.