Pipes A can fill a tank in 30 minutes while pipe B can fill it in 45
minutes. An other pipe C can empty a full tank in 60 minutes.
If all three pipes are opened simultaneously, The empty tank
will be filled in

Options

A. `2/7` hour
B. `3/7` hour
C. `4/7` hour
D. `5/7` hour

Explanation

To solve the problem, we need to determine how long it will take to fill an empty tank when three pipes (A, B, and C) are opened simultaneously. Here’s a step-by-step solution:

### Step 1: Determine the filling and emptying rates of the pipes.
- **Pipe A** can fill the tank in 30 minutes. Therefore, its rate is:
\[ \text{Rate of A} = \frac{1 \text{ tank}}{30 \text{ minutes}} = \frac{1}{30} \text{ tanks per minute} \]

- **Pipe B** can fill the tank in 45 minutes. Therefore, its rate is:
\[ \text{Rate of B} = \frac{1 \text{ tank}}{45 \text{ minutes}} = \frac{1}{45} \text{ tanks per minute} \]

- **Pipe C** can empty the tank in 60 minutes. Therefore, its rate is:
\[ \text{Rate of C} = \frac{1 \text{ tank}}{60 \text{ minutes}} = \frac{1}{60} \text{ tanks per minute} \]
Since it is emptying the tank, we will consider this rate as negative:
\[ \text{Rate of C} = -\frac{1}{60} \text{ tanks per minute} \]

### Step 2: Calculate the combined rate of all three pipes.
The combined rate when all three pipes are opened simultaneously is:
\[ \text{Combined Rate} = \text{Rate of A} + \text{Rate of B} + \text{Rate of C} \]
Substituting the values we calculated:
\[ \text{Combined Rate} = \frac{1}{30} + \frac{1}{45} - \frac{1}{60} \]

### Step 3: Find a common denominator and simplify.
The least common multiple (LCM) of 30, 45, and 60 is 180. We will convert each rate to have this common denominator:
- For Pipe A:
\[ \frac{1}{30} = \frac{6}{180} \]
- For Pipe B:
\[ \frac{1}{45} = \frac{4}{180} \]
- For Pipe C:
\[ -\frac{1}{60} = -\frac{3}{180} \]

Now, substituting these into the combined rate:
\[ \text{Combined Rate} = \frac{6}{180} + \frac{4}{180} - \frac{3}{180} = \frac{6 + 4 - 3}{180} = \frac{7}{180} \text{ tanks per minute} \]

### Step 4: Calculate the time to fill the tank.
To find the time taken to fill one tank, we take the reciprocal of the combined rate:
\[ \text{Time} = \frac{1 \text{ tank}}{\frac{7}{180} \text{ tanks per minute}} = \frac{180}{7} \text{ minutes} \]

### Step 5: Convert the time into hours and minutes.
Calculating \( \frac{180}{7} \):
\[ \frac{180}{7} \approx 25.71 \text{ minutes} \]
This can be converted into hours and minutes:
- 25 minutes and \( 0.71 \times 60 \approx 42.86 \) seconds, which is approximately 43 seconds.

Thus, the tank will be filled in approximately **25 minutes and 43 seconds**.

### Final Answer:
The empty tank will be filled in approximately **25 minutes and 43 seconds**.