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To solve this problem, let's set up equations based on the information provided.

### Given:
1. **A alone** can do the work in the same time **B and C together** can do it.
2. **A and B together** can complete the work in **10 days**.
3. **C alone** can do the work in **50 days**.

### Steps:

1. **Define work rates:**  
   - Let the total work be \( W = 1 \) (for simplicity).
   - Let \( A \)’s rate = \( a \), \( B \)’s rate = \( b \), and \( C \)’s rate = \( c \).

2. **Form equations for their rates:**  
   - Since **C can do the work in 50 days**, \( c = \frac{1}{50} \).
   - Since **A and B together** can complete the work in 10 days, \( a + b = \frac{1}{10} \).

3. **Using the condition involving A, B, and C:**
   - A’s rate is equal to the combined rate of B and C. So, \( a = b + c \).

4. **Substitute \( c = \frac{1}{50} \) into \( a = b + c \):**  
   \[
   a = b + \frac{1}{50}
   \]

5. **Substitute \( a = b + \frac{1}{50} \) into \( a + b = \frac{1}{10} \):**  
   \[
   (b + \frac{1}{50}) + b = \frac{1}{10}
   \]
   \[
   2b + \frac{1}{50} = \frac{1}{10}
   \]

6. **Solve for \( b \):**  
   \[
   2b = \frac{1}{10} - \frac{1}{50}
   \]
   Find a common denominator:
   \[
   2b = \frac{5 - 1}{50} = \frac{4}{50} = \frac{2}{25}
   \]
   \[
   b = \frac{1}{25}
   \]

### Conclusion:
B alone can complete the work in **25 days**.

**Answer: 25 days**

Would you like more details or have any other questions?

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Here are some related questions:
1. What if the time taken by C alone was different? How would that affect B's time?
2. How would the answer change if A and B together took 15 days instead of 10?
3. Can we find the time taken by A alone to do the work?
4. How would we calculate this if A, B, and C worked at different rates on different days?
5. What if B and C together took a different amount of time than given?

**Tip:** When solving work rate problems, it often helps to define the total work as 1 unit, then express individual rates as fractions of this unit.

A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in how many days?

Solve a work and time problem involving three workers: A, B, and C. Learn how to calculate the time B alone would take, given the combined rates of A with B, and C alone. Detailed step-by-step solution suitable for Grades 9-10.

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