Pipe A takes 4 hours to fill a tank. Pipe B tankes 6 hours to empty the same tank when full. If both the Pipe are opened at the same time when tank is empty, how many hours will it take for the tank to fill?

Options

A. 10
B. 8
C. 12
D. 15

Answer

To solve the problem, we need to determine how long it will take to fill the tank when both Pipe A (which fills the tank) and Pipe B (which empties the tank) are opened at the same time.

### Step-by-Step Solution:

1. **Determine the Capacity of the Tank:**
- Let's assume the capacity of the tank is 12 units (this is the least common multiple of the filling and emptying times, which makes calculations easier).

2. **Calculate the Filling Rate of Pipe A:**
- Pipe A takes 4 hours to fill the tank.
- Therefore, in 1 hour, Pipe A fills \( \frac{12 \text{ units}}{4 \text{ hours}} = 3 \text{ units/hour} \).

3. **Calculate the Emptying Rate of Pipe B:**
- Pipe B takes 6 hours to empty the tank.
- Therefore, in 1 hour, Pipe B empties \( \frac{12 \text{ units}}{6 \text{ hours}} = 2 \text{ units/hour} \).

4. **Determine the Combined Rate of Both Pipes:**
- When both pipes are opened, the net effect on the tank is:
\[ \text{Net Rate} = \text{Rate of Pipe A} - \text{Rate of Pipe B} = 3 \text{ units/hour} - 2 \text{ units/hour} = 1 \text{ unit/hour} \]

5. **Calculate the Time to Fill the Tank:**
- The time taken to fill the tank can be calculated using the formula:
\[ \text{Time} = \frac{\text{Capacity of the tank}}{\text{Net Rate}} = \frac{12 \text{ units}}{1 \text{ unit/hour}} = 12 \text{ hours} \]

### Final Answer:
The tank will take **12 hours** to fill when both pipes are opened at the same time.

---