Explanation:

- Total work by 5 men: 5 men complete work in 16 days. Thus, total work = 5 × 16 = 80 man-days.

- Work rate of 1 man: 80 man-days / 5 = 16 days.

- Total work by 8 women: 8 women complete work in 36 days. Thus, total work = 8 × 36 = 288 woman-days.

- Work rate of 1 woman: 288 woman-days / 8 = 36 days.

- Equivalent men to women work rate: 1 man's work rate for 1 day = 36/16 = 2.25 times a woman's daily rate.

- Initial work by 10 men for 4 days: Work done = 10 men × 4 days = 40 man-days. Remaining work = 80 - 40 = 40 man-days.

- Work when 12 women join: Convert 12 women to equivalent men = 12 / 2.25 = approximately 5.33 men.

- Effective workforce now: 10 men + 5.33 men (women equivalent) = 15.33 men.

- Remaining work completed by combined workforce: Time = 40 man-days / 15.33 men ˜ 2.61 days.

- Total time: 4 days + 2.61 days ˜ 6.61 days, which can be rounded to 7 days.

Correct Answer: ? Option 3 - 7