6 men can complete a piece of work in 9 days, while 6 women can do it in 6 days. In how many days can 2 women and 3 men complete this work?

Correct option is D

Given:

6 men complete the work in 9 days

6 women complete the work in 6 days

Find time taken by 3 men + 2 women

Formula Used:

Total work = $$M_1\times E_1 \times D_1 = M_2\times E_2 \times D_2$$ 

where M = number of men, D = number of days, E = Efficiency

Solution:

Using the formula; 

6M × 9 = 6W × 6 

54M = 36B 

​$$\frac{M}{W} = \frac{36}{54} =\frac{6}{9}$$ 

so, 1 man efficiency = 6 and 1 woman efficiency = 9

Now, time taken by 3men + 2 women 

(3M + 2W)×D = 6M × 9 

{3(6) + 2(9)}×D = 6(6) × 9

{18+ 18} × D = 36 × 9 

36 × D = 36 ×9 

D = 9 days