Two pipes X and Y can fill a tank in 6 hours and 8 hours respectively while another pipe Z can empty the tank in 4.8 hours. If all the three pipes are opened at the same time, then the time in which the tank can be filled.

Answer

To solve the problem, we need to determine how long it will take to fill the tank when all three pipes (X, Y, and Z) are opened at the same time.

### Step-by-Step Solution:

1. **Determine the filling rates of pipes X and Y**:
- Pipe X can fill the tank in 6 hours. Therefore, the rate of pipe X is:
\[ \text{Rate of X} = \frac{1 \text{ tank}}{6 \text{ hours}} = \frac{1}{6} \text{ tanks per hour} \]
- Pipe Y can fill the tank in 8 hours. Therefore, the rate of pipe Y is:
\[ \text{Rate of Y} = \frac{1 \text{ tank}}{8 \text{ hours}} = \frac{1}{8} \text{ tanks per hour} \]

2. **Determine the emptying rate of pipe Z**:
- Pipe Z can empty the tank in 4.8 hours. Therefore, the rate of pipe Z is:
\[ \text{Rate of Z} = \frac{1 \text{ tank}}{4.8 \text{ hours}} = \frac{1}{4.8} \text{ tanks per hour} \]
- To express this in a simpler form, we can convert 4.8 hours to a fraction:
\[ \frac{1}{4.8} = \frac{1}{\frac{24}{5}} = \frac{5}{24} \text{ tanks per hour} \]

3. **Calculate the combined rate of filling when all pipes are opened**:
- The combined rate when all three pipes are opened is:
\[ \text{Combined Rate} = \text{Rate of X} + \text{Rate of Y} - \text{Rate of Z} \]
- Substituting the values:
\[ \text{Combined Rate} = \frac{1}{6} + \frac{1}{8} - \frac{5}{24} \]

4. **Finding a common denominator**:
- The least common multiple (LCM) of 6, 8, and 24 is 24. We convert each rate:
\[ \frac{1}{6} = \frac{4}{24}, \quad \frac{1}{8} = \frac{3}{24}, \quad \frac{5}{24} = \frac{5}{24} \]
- Now substituting these values:
\[ \text{Combined Rate} = \frac{4}{24} + \frac{3}{24} - \frac{5}{24} = \frac{4 + 3 - 5}{24} = \frac{2}{24} = \frac{1}{12} \text{ tanks per hour} \]

5. **Calculate the time to fill the tank**:
- If the combined rate is \(\frac{1}{12}\) tanks per hour, then the time taken to fill 1 tank is the reciprocal of the rate:
\[ \text{Time} = \frac{1 \text{ tank}}{\frac{1}{12} \text{ tanks per hour}} = 12 \text{ hours} \]

### Final Answer:
The time taken to fill the tank when all three pipes are opened together is **12 hours**.