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The problem you've provided involves a comparison of the work rates of men and women and requires us to calculate the time needed for a different group of workers to finish the same task.

### Step-by-step solution:

1. **Group 1 (6 men and 8 women) finishes the job in 10 days:**
   \[
   (6 \text{ men} + 8 \text{ women}) \times 10 \text{ days} = \text{Total work}.
   \]

2. **Group 2 (26 men and 48 women) finishes the job in 2 days:**
   \[
   (26 \text{ men} + 48 \text{ women}) \times 2 \text{ days} = \text{Total work}.
   \]

   Since both groups complete the same job, the amount of work done by each group should be equal.

3. Now, let's establish the ratio of work rates for men and women based on these two situations. We assume that the work rate of one man is \( M \) and the work rate of one woman is \( W \). So, we set up the equation for total work done:

   \[
   (6M + 8W) \times 10 = (26M + 48W) \times 2.
   \]

4. Simplifying both sides:
   \[
   60M + 80W = 52M + 96W.
   \]

5. Rearranging terms:
   \[
   60M - 52M = 96W - 80W,
   \]
   \[
   8M = 16W,
   \]
   \[
   M = 2W.
   \]

   Therefore, one man works at twice the rate of one woman.

6. **Now, consider the third group with 15 men and 20 women:**

   \[
   15M + 20W = 15(2W) + 20W = 30W + 20W = 50W.
   \]

7. To find the number of days required by this group, let's use the total work calculated from the first group:
   \[
   (6M + 8W) \times 10 = (6(2W) + 8W) \times 10 = (12W + 8W) \times 10 = 20W \times 10 = 200W.
   \]

   The total amount of work is \( 200W \). Now, the third group with a work rate of \( 50W \) per day will take:
   \[
   \frac{200W}{50W} = 4 \text{ days}.
   \]

Thus, the time required for the third group (15 men and 20 women) to complete the task is **4 days**.

### Final answer: **B. 4 days**

Would you like further details on any step?

### Related Questions:
1. How would the time change if there were more men than women in the third group?
2. Can you calculate the time needed if only 10 men worked on this job?
3. How would you adjust the calculation if the work rate of women was different?
4. What would happen if the second group worked for 3 days instead of 2 days?
5. If the work rate of men and women increased by 10%, how would the results change?

**Tip**: When solving work-rate problems, expressing the work done by each group in terms of a common unit, like \( W \) for women's work, simplifies the comparison.

Jika 6 orang laki-laki dan 8 orang perempuan dapat menyelesaikan suatu pekerjaan dalam 10 hari, sedangkan 26 orang laki-laki dan 48 perempuan dapat menyelesaikan pekerjaan yang sama dalam 2 hari, maka waktu yang dibutuhkan oleh 15 orang laki-laki dan 20 orang perempuan untuk menyelesaikan jenis pekerjaan yang sama adalah?

Learn how to solve a work-rate problem involving 6 men and 8 women completing a task in 10 days, and 26 men and 48 women in 2 days. This example demonstrates key concepts in algebra and ratios to find the time needed for 15 men and 20 women to complete the same task.

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