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?

• A. $$8\frac{9}{{13}}$$
• B. $$6\frac{9}{{13}}$$
• C. $$5\frac{9}{{13}}$$
• D. $$7\frac{9}{{13}}$$

Answer 1

Answer:

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

Shortcut Trick

Let the efficiency of 1 man be M And the efficiency of 1 woman be W 

So, According to the formula work = Efficiency × Time 

Total work = 10M × 10 = 12W × 10

M : W = 6 : 5

Now, Total work = 100 M = 100 × 6 = 600 units

Total efficiency of 8 men and 6 women = 8M + 6W

⇒ 8 × 6 + 6 × 5 = 78 unit/day 

So, Time = Work/Efficiency

⇒ Time = 600/78 days = 100/13 days

8 men and 6 women can complete a work in $7\frac{9}{{13}}$

Alternate Method 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 the number of days work done by men 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

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

8 men and 6 women can complete a work in $7\frac{9}{13}days$