3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to finish the work ?

Solution (By Examveda Team)

According to the question,
3 men = 5 women
As they complete the same work in same time
6 men + 5 women
= 6 men + 3 men
= 9 men
If, 3 men does a work in 12 days
1 men does a work in 12 × 3
9 men does a work in $$\frac{{{\text{12}} \times {\text{3}}}}{9}$$  = 4 days

Alternate :
$$\eqalign{ & 3{\text{ men}} \times {\text{12}} = {\text{5 women}} \times {\text{12}} \cr & \frac{{{\text{men}}}}{{{\text{women}}}} = \frac{5}{3} \cr & {\text{Total work}} \cr & = 3 \times 5 \times 12 \cr & = 15 \times 12 \cr & = 180{\text{ units}} \cr & {\text{Efficiency of 6 men}} + {\text{5 women}} \cr & = 6 \times 5 + 5 \times 3 \cr & = 45 \cr & {\text{Time taken by 6 men}} + {\text{5 women}} \cr & = \frac{{180}}{{45}} \cr & = 4{\text{ days}} \cr} $$