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 ?

1 $3 \frac{1}{2} days$ ${\text{3}}\frac{1}{2}{\text{ days}}$
2 $3 \frac{3}{4} days$ ${\text{3}}\frac{3}{4}{\text{ days}}$
3 $4 days$ ${\text{4 days}}$
4 $5 days$ ${\text{5 days}}$

Answer:- 1

Explanation:-

Solution:

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)

\begin{aligned} ∴ 32 : 6 :: 20 : x \\ \Leftrightarrow x = (\frac{6 \times 20}{32}) \\ \Leftrightarrow x = \frac{15}{4} \\ \Leftrightarrow x = 3 \frac{3}{4} \end{aligned}

$\eqalign{ & \therefore {\text{ }}32:6::20:x \cr & \Leftrightarrow x = \left( {\frac{{6 \times 20}}{{32}}} \right) \cr & \Leftrightarrow x = \frac{{15}}{4} \cr & \Leftrightarrow x = 3\frac{3}{4} \cr}$