3 men or 6 women can do a piece of work in 20 days. In how days will 12 men and 8 women do the same work ?

A. $${\text{3}}\frac{1}{2}{\text{ days}}$$

B. $${\text{3}}\frac{3}{4}{\text{ days}}$$

C. \[{\text{4 days}}\]

D. \[{\text{5 days}}\]

Answer: Option B

Solution(By Examveda Team)

Let the required number of days be x
3 men = 6 women
⇒12 men = (2 × 12) women = 24 women
∴ 12 men and 8 women = (24 + 8) women = 32 women
Now, More women, Less days (Indirect Proportion)
$$\eqalign{ & \therefore {\text{ }}32:6::20:x \cr & \Leftrightarrow x = \left( {\frac{{6 \times 20}}{{32}}} \right) \cr & \Leftrightarrow x = \frac{{15}}{4} \cr & \Leftrightarrow x = 3\frac{3}{4} \cr} $$