Given:
- 4 men and 6 women can complete the work in 8 days.
- 3 men and 7 women can complete the work in 10 days.

Let's assume that the work requires x days for 1 man to complete and y days for 1 woman to complete.

Calculation:
- In 1 day, 1 man can complete 1/x of the work and 1 woman can complete 1/y of the work.
- Therefore, in 1 day, 4 men can complete 4/x of the work and 6 women can complete 6/y of the work.
- According to the first statement, 4 men and 6 women can complete the work in 8 days.
- So, in 1 day, 4 men and 6 women can complete 1/8 of the work.

From the above calculations, we can form the following equation:
4/x + 6/y = 1/8 .............(1)

- Similarly, in 1 day, 3 men can complete 3/x of the work and 7 women can complete 7/y of the work.
- According to the second statement, 3 men and 7 women can complete the work in 10 days.
- So, in 1 day, 3 men and 7 women can complete 1/10 of the work.

From the above calculations, we can form the following equation:
3/x + 7/y = 1/10 .............(2)

Now, we need to solve equations (1) and (2) to find the values of x and y.

Solving these equations simultaneously, we get:
x = 16 days and y = 28 days

Explanation:
- This means that 1 man can complete the work in 16 days and 1 woman can complete the work in 28 days.
- We need to find how many days 10 women will take to complete the work.
- In 1 day, 10 women can complete 10/y of the work.
- Substituting the value of y, we get:
10/28 = 5/14

Therefore, 10 women will take 14/5 days to complete the work.

Converting this to the nearest whole number, we get:
14/5 ≈ 2.8

So, 10 women will take approximately 3 days to complete the work.

Hence, the correct answer is option (A) 40 days.