8 men and 4 boys can finish a piece of work in 5 days. 6 women and 8 boys can finish the same work in 5 days. Also, 4 men and 6 women can finish the same work in 5 days. In how many days can 2 men, 3 women and 10 boys finish the same work at their double efficiency?

This problem can be solved by using the concept of man-days.

Step 1: Let's denote the work done by one man in one day as M, the work done by one woman in one day as W, and the work done by one boy in one day as B.

Step 2: From the problem, we have the following equations:

8M + 4B = 5 (equation 1) (since 8 men and 4 boys can finish the work in 5 days)

6W + 8B = 5 (equation 2) (since 6 women and 8 boys can finish the work in 5 days)

4M + 6W = 5 (equation 3) (since 4 men and 6 women can finish the work in 5 days)

Step 3: We can solve these equations simultaneously to find the values of M, W, and B.

Step 4: Once we have the values of M, W, and B, we can find out how many days 2 men, 3 women, and 10 boys can finish the work at their double efficiency.

The efficiency of 2 men, 3 women, and 10 boys is 2M + 3W + 10B. Since their efficiency is doubled, the total efficiency is 2(2M + 3W + 10B).

Step 5: The number of days required to finish the work is the total work divided by the total efficiency.

Please note that without the actual values of M, W, and B, we cannot calculate the exact number of days. However, the method described above is the correct approach to solve this problem.