Pipe 'A' & 'B' can fill a tank in 10h & 12h respectively but pipe 'C' can empty the same tank in 15h. In how much time it will take fill the tank when the three pipes are opened together?

Answer

To solve the problem, we need to calculate the rates at which each pipe fills or empties the tank and then combine these rates to find out how long it will take to fill the tank when all three pipes are opened together.

### Step-by-Step Solution:

1. **Calculate the filling rate of Pipe A:**
- Pipe A can fill the tank in 10 hours.
- Therefore, the rate of Pipe A = 1 tank / 10 hours = 0.1 tanks per hour.

2. **Calculate the filling rate of Pipe B:**
- Pipe B can fill the tank in 12 hours.
- Therefore, the rate of Pipe B = 1 tank / 12 hours = 0.0833 tanks per hour (or 5/60 tanks per hour).

3. **Calculate the emptying rate of Pipe C:**
- Pipe C can empty the tank in 15 hours.
- Therefore, the rate of Pipe C = 1 tank / 15 hours = 0.0667 tanks per hour (or 4/60 tanks per hour).

4. **Combine the rates of all three pipes:**
- The combined rate when all pipes are opened together:
\[ \text{Combined Rate} = \text{Rate of A} + \text{Rate of B} - \text{Rate of C} \]
\[ = 0.1 + 0.0833 - 0.0667 \]
\[ = 0.1166 \text{ tanks per hour} \]

5. **Calculate the time to fill the tank:**
- To find the time taken to fill 1 tank:
\[ \text{Time} = \frac{1 \text{ tank}}{\text{Combined Rate}} = \frac{1}{0.1166} \approx 8.57 \text{ hours} \]

### Final Answer:
It will take approximately **8.57 hours** to fill the tank when all three pipes are opened together.