# 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,

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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. $7\frac{9}{{13}}$

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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.