If 4 men or 8 women can do a piece of work in 15 days, in how many days can 6 men and 12 women do the same piece of work?

Options

A. 1) 10 day / 10 दिन
B. 2) 15 day / 15 दिन
C. 3) 30 day / 30 दिन
D. 4) 20 day / 20 दिन

Explanation

To solve the problem, we start by determining the work done by men and women.

1. **Determine the work done by 4 men in 15 days:**
- If 4 men can complete the work in 15 days, then the total work can be expressed in man-days.
- Total work = Number of men × Number of days = 4 men × 15 days = 60 man-days.

2. **Determine the work done by 1 man in 1 day:**
- Since 4 men can do 60 man-days of work, 1 man can do:
- Work done by 1 man in 1 day = Total work / Number of men = 60 man-days / 4 men = 15 man-days per man.

3. **Determine the work done by 8 women in 15 days:**
- The problem states that 8 women can also complete the same work in 15 days, which means:
- Total work = Number of women × Number of days = 8 women × 15 days = 120 woman-days.

4. **Determine the work done by 1 woman in 1 day:**
- Since 8 women can do 120 woman-days of work, 1 woman can do:
- Work done by 1 woman in 1 day = Total work / Number of women = 120 woman-days / 8 women = 15 woman-days per woman.

5. **Establish the relationship between men and women:**
- From our calculations, we see that 1 man does the same amount of work in a day as 2 women (since 15 man-days = 30 woman-days).

6. **Calculate the total work done by 6 men and 12 women in 1 day:**
- Work done by 6 men in 1 day = 6 men × 15 man-days = 90 man-days.
- Work done by 12 women in 1 day = 12 women × 7.5 woman-days = 90 woman-days (since 1 woman does 7.5 woman-days).
- Total work done by 6 men and 12 women in 1 day = 90 man-days + 90 woman-days = 180 man-days.

7. **Calculate the number of days required to complete the work:**
- Total work = 60 man-days.
- Days required = Total work / Total work done in 1 day = 60 man-days / 180 man-days = 1/3 days.

Thus, 6 men and 12 women can complete the work in **1/3 of a day**.