Question

10 men can finish a piece of work in 10 days, whereas it takes 12 women to finish it in 10 days. If 8 men and 6 women undertake to complete the work, then in how many days will they complete it?
1. \(8\frac{9}{{13}}\)
2. \(6\frac{9}{{13}}\)
3. \(5\frac{9}{{13}}\)
4. \(7\frac{9}{{13}}\)

Answer 1

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.