Pipe A can fill a tank in 36 minutes and pipe B can fill it in 45 minutes. If both the pipes are opened to fill an empty tank, in how many minutes will it be full?

Options

A. 15
B. 18
C. 20
D. 25

Answer

To solve the problem of how long it will take for both Pipe A and Pipe B to fill the tank together, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the filling rates of each pipe**:
- Pipe A can fill the tank in 36 minutes.
- Pipe B can fill the tank in 45 minutes.

2. **Calculate the capacity of the tank**:
- We can assume the capacity of the tank to be the least common multiple (LCM) of the times taken by both pipes to fill the tank.
- LCM of 36 and 45 is 180 units.

3. **Calculate the filling rate of Pipe A**:
- If Pipe A fills 180 units in 36 minutes, then in 1 minute, it fills:
\[ \text{Rate of Pipe A} = \frac{180 \text{ units}}{36 \text{ minutes}} = 5 \text{ units per minute} \]

4. **Calculate the filling rate of Pipe B**:
- If Pipe B fills 180 units in 45 minutes, then in 1 minute, it fills:
\[ \text{Rate of Pipe B} = \frac{180 \text{ units}}{45 \text{ minutes}} = 4 \text{ units per minute} \]

5. **Calculate the combined filling rate of both pipes**:
- When both pipes are opened together, their combined filling rate is:
\[ \text{Combined Rate} = \text{Rate of Pipe A} + \text{Rate of Pipe B} = 5 + 4 = 9 \text{ units per minute} \]

6. **Calculate the time taken to fill the tank when both pipes are open**:
- The time taken to fill the tank can be calculated using the formula:
\[ \text{Time} = \frac{\text{Capacity of the tank}}{\text{Combined Rate}} = \frac{180 \text{ units}}{9 \text{ units per minute}} = 20 \text{ minutes} \]

### Final Answer:
Thus, the tank will be full in **20 minutes** when both pipes are opened together.

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