12 Men or 15 women can do a piece of work in
21 days. Find the number of days required to
complete the same work by 6 men and
10 women.

To solve this, we first need to determine the work done by one man and one woman. If 12 men or 15 women can complete the work in 21 days, we can calculate their work rates.

Let’s use the concept of work done.
In terms of man-days:
12 men × 21 days = 252 man-days.
In terms of woman-days:
15 women × 21 days = 315 woman-days.

So, 1 man works at a rate of 1/252 of the work per day, and 1 woman works at a rate of 1/315 of the work per day.

Now, let’s find the combined work rate of 6 men and 10 women:

Work rate of 6 men:
6 men × (1/252) work/day = 6/252 = 1/42 work/day.

Work rate of 10 women:
10 women × (1/315) work/day = 10/315 = 2/63 work/day.

Now, we need a common denominator to add these rates:
LCM of 42 and 63 is 126.
Converting:
1/42 = 3/126
2/63 = 4/126

Adding these together, the total work rate:
3/126 + 4/126 = 7/126 = 1/18 work/day.

Thus, the number of days required to complete the work by 6 men and 10 women is the reciprocal of the work rate:
Days = 1 / (1/18) = 18 days.

So, 6 men and 10 women can complete the work in 18 days!