To fill a cistern, pipes A, B & C takes 20, 15 and 12 minutes respectively. The time in minutes that the three pipes together will take to fill a cistern is ?

Answer

To solve the problem of how long it will take for pipes A, B, and C to fill a cistern together, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Total Work**:
Since the pipes take different times to fill the cistern, we can assume the total work to fill the cistern is 60 units (this is a common multiple of the times given).

2. **Calculate the Efficiency of Each Pipe**:
- **Efficiency of Pipe A**:
\[ \text{Efficiency of A} = \frac{60 \text{ units}}{20 \text{ minutes}} = 3 \text{ units per minute} \]
- **Efficiency of Pipe B**:
\[ \text{Efficiency of B} = \frac{60 \text{ units}}{15 \text{ minutes}} = 4 \text{ units per minute} \]
- **Efficiency of Pipe C**:
\[ \text{Efficiency of C} = \frac{60 \text{ units}}{12 \text{ minutes}} = 5 \text{ units per minute} \]

3. **Calculate the Combined Efficiency**:
Now, we add the efficiencies of all three pipes:
\[ \text{Combined Efficiency} = \text{Efficiency of A} + \text{Efficiency of B} + \text{Efficiency of C} = 3 + 4 + 5 = 12 \text{ units per minute} \]

4. **Calculate the Time Taken to Fill the Cistern**:
To find the time taken to fill the cistern when all three pipes are working together, we use the formula:
\[ \text{Time} = \frac{\text{Total Work}}{\text{Combined Efficiency}} = \frac{60 \text{ units}}{12 \text{ units per minute}} = 5 \text{ minutes} \]

### Final Answer:
The time taken by the three pipes together to fill the cistern is **5 minutes**.