Two pipes can independently fill a bucket in 20 minutes and 25 minutes. Both are opened together for 5 minutes after which the second pipe is turned off. What is the time taken by the first pipe alone to fill the remaining portion of the bucket?

Options

A. 11 minutes
B. 16 minutes
C. 20 minutes
D. 15 minutes

Answer

To solve the problem, we need to determine how much of the bucket is filled after both pipes are opened together for 5 minutes, and then calculate how long it takes for the first pipe to fill the remaining portion of the bucket.

### Step-by-Step Solution:

1. **Determine the rates of the pipes:**
- Pipe A fills the bucket in 20 minutes. Therefore, the rate of Pipe A is:
\[ \text{Rate of A} = \frac{1 \text{ bucket}}{20 \text{ minutes}} = \frac{1}{20} \text{ buckets per minute} \]
- Pipe B fills the bucket in 25 minutes. Therefore, the rate of Pipe B is:
\[ \text{Rate of B} = \frac{1 \text{ bucket}}{25 \text{ minutes}} = \frac{1}{25} \text{ buckets per minute} \]

2. **Calculate the combined rate of both pipes:**
- When both pipes are opened together, their rates add up:
\[ \text{Combined Rate} = \text{Rate of A} + \text{Rate of B} = \frac{1}{20} + \frac{1}{25} \]
- To add these fractions, find a common denominator, which is 100:
\[ \frac{1}{20} = \frac{5}{100}, \quad \frac{1}{25} = \frac{4}{100} \]
- Thus, the combined rate is:
\[ \text{Combined Rate} = \frac{5}{100} + \frac{4}{100} = \frac{9}{100} \text{ buckets per minute} \]

3. **Calculate the amount filled in 5 minutes:**
- In 5 minutes, the amount of the bucket filled by both pipes is:
\[ \text{Amount filled} = \text{Combined Rate} \times 5 = \frac{9}{100} \times 5 = \frac{45}{100} = 0.45 \text{ buckets} \]

4. **Determine the remaining portion of the bucket:**
- Since the total bucket capacity is 1 bucket, the remaining portion is:
\[ \text{Remaining portion} = 1 - 0.45 = 0.55 \text{ buckets} \]

5. **Calculate the time taken by Pipe A to fill the remaining portion:**
- The time taken by Pipe A to fill the remaining 0.55 buckets is calculated using its rate:
\[ \text{Time} = \frac{\text{Remaining portion}}{\text{Rate of A}} = \frac{0.55}{\frac{1}{20}} = 0.55 \times 20 = 11 \text{ minutes} \]

### Final Answer:
The time taken by the first pipe alone to fill the remaining portion of the bucket is **11 minutes**.