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 ?

Answer: Option C

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