2 men and 3 women can finish the work in 10 days, while 4 men can do it in 10 days. 3 men and 3 women will finish the work in?

Correct option is D

Given:
2 men and 3 women can finish the work in 10 days.
4 men can finish the work in 10 days.
Formula Used:

$$\text{Time} = \frac{1}{\text{Work rate}}$$​​

Solution:
Let the work rate of 1 man be M and the work rate of 1 woman be W .
2 men and 3 women can finish the work in 10 days:
$$(2M + 3W) \times 10 = 1 \text{ (total work)}.$$​​
$$20M + 30W = 1. \quad \text{(Equation 1)}$$​
4 men can finish the work in 10 days:
$$4M \times 10 = 1 \text{ (total work)}.$$​​
$$40M = 1. \quad \text{(Equation 2)}$$​​
​$$M = \frac{1}{40}.$$​​
 $$20M + 30W = 1 \\20 \times \frac{1}{40} + 30W = 1 \\\frac{1}{2} + 30W = 1 \\$$​​

$$30W = 1 - \frac{1}{2} \\$$​

$$30W = \frac{1}{2} \\$$​
W $$= \frac{1}{60}.$$​
Thus, the work rate of 1 woman is  $$\frac{1}{60}$$ of the work per day.
Calculate the combined work rate of 3 men and 3 women.
​$$3M + 3W = 3 \times \frac{1}{40} + 3 \times \frac{1}{60} = \frac{3}{40} + \frac{3}{60}.$$

​​$$\frac{3}{40} + \frac{1}{20} = \frac{3}{40} + \frac{2}{40} = \frac{5}{40} = \frac{1}{8}.$$​
Thus, the combined work rate of 3 men and 3 women is $$\frac{1}{8}$$ of the work per day.
Calculate the time required to complete the work.
​$$\text{Time} = \frac{1}{\text{Work rate}} = \frac{1}{\frac{1}{8}} = 8 \text{ days}.$$​​
3 men and 3 women will finish the work in 8 days.