If `4//5^(th)` of a cistern is filled in 20 minute, then what is the time (in minutes) needed to fill the remaining part?

Options

A. 5
B. 10
C. 12
D. 15

Answer

To solve the problem, we need to determine how long it will take to fill the remaining part of the cistern after 4/5 of it has already been filled in 20 minutes.

### Step-by-Step Solution:

1. **Understand the Problem**: We know that 4/5 of the cistern is filled in 20 minutes. We need to find out how long it will take to fill the remaining 1/5 of the cistern.

2. **Calculate the Time to Fill the Whole Cistern**:
- If 4/5 of the cistern is filled in 20 minutes, we can determine the time it takes to fill the entire cistern.
- Let the total time to fill the whole cistern be \( T \).
- Since 4/5 of the cistern takes 20 minutes, we can set up the equation:
\[ \frac{4}{5}T = 20 \]
- To find \( T \), we can rearrange the equation:
\[ T = 20 \times \frac{5}{4} = 25 \text{ minutes} \]

3. **Determine the Remaining Part**:
- The remaining part of the cistern is 1/5 of the total cistern.
- Since the total time to fill the cistern is 25 minutes, we can find the time to fill the remaining 1/5 by calculating:
\[ \text{Time to fill } \frac{1}{5} \text{ of the cistern} = \frac{1}{5}T = \frac{1}{5} \times 25 = 5 \text{ minutes} \]

4. **Conclusion**:
- Therefore, the time needed to fill the remaining part of the cistern is 5 minutes.

### Final Answer:
The time needed to fill the remaining part of the cistern is **5 minutes**.