8) 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days . in how many days will 10 women complete it ?

Let's solve this step by step:

Step 1: Let's assume the work done by one man in one day is m and the work done by one woman in one day is w.

Step 2: According to the problem, we can form two equations based on the given information.

From "4 men and 6 women can complete a work in 8 days", we get: 8(4m + 6w) = 1 ----(equation 1)

From "3 men and 7 women can complete it in 10 days", we get: 10(3m + 7w) = 1 ----(equation 2)

Step 3: Now, we have two equations, and we can solve them simultaneously to find the values of m and w.

Step 4: Multiply equation 1 by 3 and equation 2 by 4 and subtract equation 2 from equation 1, we get: w = 1/240

Step 5: Substitute w = 1/240 in equation 1, we get: m = 1/120

Step 6: Now, we are asked to find "in how many days will 10 women complete it". We can find this by dividing the total work (which is 1) by the work done by 10 women in one day (which is 10w).

So, the number of days 10 women will take to complete the work is 1/(10w) = 1/(10*1/240) = 24 days.