3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to finish the work?
3 पुरुष या 5 स्त्रियाँ एक कार्य 12 दिनों में पूरा कर सकते हैं। तदनुसार, 6 पुरुषों तथा 5 स्त्रियों को वही कार्य पूरा करने में कितना समय लगेगा?

Options

A. 4 days/ 4 दिन
B. 5 days/ 5 दिन
C. 6 day/ 6 दिन
D. 7 days/ 7 दिन

Explanation

To solve the problem, we need to determine how long it will take for 6 men and 5 women to complete the same work that 3 men or 5 women can do in 12 days.

### Step-by-Step Solution:

1. **Determine the total work done in terms of man-days or woman-days.**
- Given that 3 men can complete the work in 12 days, we can calculate the total work in terms of man-days.
- Total work = Number of men × Number of days = 3 men × 12 days = 36 man-days.

2. **Calculate the work done by women.**
- Similarly, we can calculate the total work in terms of woman-days.
- Given that 5 women can complete the work in 12 days, Total work = Number of women × Number of days = 5 women × 12 days = 60 woman-days.

3. **Establish a relationship between the work done by men and women.**
- From the above calculations, we can see that 36 man-days = 60 woman-days.
- Therefore, 1 man-day = 60/36 woman-days = 5/3 woman-days.
- This means that 1 man does the work equivalent to 5/3 women in one day.

4. **Calculate the work done by 6 men and 5 women in one day.**
- Work done by 6 men in one day = 6 men × (3/5) woman-days = 6 × (3/5) = 18/5 woman-days.
- Work done by 5 women in one day = 5 woman-days.
- Total work done by 6 men and 5 women in one day = (18/5 + 5) woman-days = (18/5 + 25/5) = 43/5 woman-days.

5. **Determine how many days it will take for 6 men and 5 women to complete the work.**
- Total work is 60 woman-days (from step 2).
- Days required = Total work / Work done in one day = 60 woman-days / (43/5 woman-days) = 60 × (5/43) = 300/43 days.

6. **Convert the result to a more understandable form.**
- 300/43 days is approximately 6.98 days.
- Therefore, it will take about 7 days for 6 men and 5 women to finish the work.

### Final Answer:
6 men and 5 women will take approximately 7 days to finish the work.