The average age of a combined group of men and women is 25 years. If the average age of the group of men is 26 years and the of the group of women is 21 years, then the percentage of men and women in the group is respectively.
(a)20,80
(b)40,50
(c)60,40
(d)80,20

Options

A. 20,80
B. 40,50
C. 60,40
D. 80,20

Answer

To solve the problem, we will use the method of alligation to find the percentage of men and women in the group based on their average ages.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Average age of the combined group (men and women) = 25 years
- Average age of men = 26 years
- Average age of women = 21 years

2. **Set Up the Alligation:**
- We will use the alligation method to find the ratio of men to women.
- The formula for alligation is:
\[ \text{Difference between men's average and overall average} = 26 - 25 = 1 \]
\[ \text{Difference between women's average and overall average} = 25 - 21 = 4 \]

3. **Calculate the Ratio:**
- The ratio of men to women can be expressed as:
\[ \text{Men : Women} = 4 : 1 \]

4. **Total Parts in the Ratio:**
- Total parts = 4 (for men) + 1 (for women) = 5 parts

5. **Calculate the Percentage of Men:**
- Percentage of men = \(\frac{\text{Men's part}}{\text{Total parts}} \times 100\)
- Percentage of men = \(\frac{4}{5} \times 100 = 80\%\)

6. **Calculate the Percentage of Women:**
- Percentage of women = \(\frac{\text{Women's part}}{\text{Total parts}} \times 100\)
- Percentage of women = \(\frac{1}{5} \times 100 = 20\%\)

7. **Final Result:**
- The percentage of men is 80% and the percentage of women is 20%.

### Conclusion:
The percentages of men and women in the group are respectively:
- Men: 80%
- Women: 20%

Thus, the correct answer is **(d) 80, 20**.