A pipe can fill a tank in 6 hours and another pipe can empty the tank in 12 hours. If both the pipes are opened at the same time,the tank can be filled in

Options

A. 10hr
B. 12hr
C. 14hr
D. 16hr

Answer

To solve the problem, we need to determine how long it will take to fill a tank when one pipe is filling it and another pipe is emptying it.

### Step-by-Step Solution:

1. **Identify the rates of the pipes**:
- Let pipe A be the filling pipe, which can fill the tank in 6 hours.
- Let pipe B be the emptying pipe, which can empty the tank in 12 hours.

2. **Calculate the filling rate of pipe A**:
- The rate of filling by pipe A is \( \frac{1 \text{ tank}}{6 \text{ hours}} = \frac{1}{6} \text{ tanks per hour} \).

3. **Calculate the emptying rate of pipe B**:
- The rate of emptying by pipe B is \( \frac{1 \text{ tank}}{12 \text{ hours}} = \frac{1}{12} \text{ tanks per hour} \).

4. **Combine the rates of both pipes**:
- Since pipe A is filling and pipe B is emptying, we combine their rates:
\[ \text{Net rate} = \text{Rate of A} - \text{Rate of B} = \frac{1}{6} - \frac{1}{12} \]

5. **Find a common denominator to combine the rates**:
- The least common multiple (LCM) of 6 and 12 is 12. Thus, we rewrite the rates:
\[ \frac{1}{6} = \frac{2}{12} \]
- Now, substituting back:
\[ \text{Net rate} = \frac{2}{12} - \frac{1}{12} = \frac{1}{12} \text{ tanks per hour} \]

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

### Final Answer:
The tank can be filled in **12 hours** when both pipes are opened at the same time.

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