Correct Answer - Option 4 :

\(7\frac{9}{{13}}\)
**Given:**

10 men can finish a piece of work = 10 days

12 women can finish a piece of work = 10 days

**Calculations:**

1 man can complete a piece of work = 10 × 10

⇒ 100 days

1 woman can finish a piece of work = 12 × 10

⇒ 120 days

The ratio of number of days work done by man and women = 100 ∶ 120

⇒ 5 ∶ 6

1 woman =5/6 men

8 men and 6 women = 8 men + 6 × 5/6 men

⇒ 8 men + 5 men = 13 men

13 men can complete work in = 10 × 10/13

⇒ \(7{9 \over 13}\) days

**∴ 8 men and 6 women can complete a work in \(7{9 \over 13}\) days.**