According to the question,

6 men = 10 women

∴ 1 man =$\frac{10}{6}$or $\frac{5}{3}$women

Now, 12 men + 10 women$=12\times \frac{5}{3}$women+ 10 women

                ⇒ 20 women+ 10 women = 30 women

According to the formula,

M₁ D₁ W₂ = M₂ D₂ W₁

Here,

M₁ = 10, D₁ =24, W₁ =1,

M₂ = 30, D₂ = ?, W₂ = 1 

$$\begin{gathered} \Rightarrow 10\times 24\times 1=30\times D_2\times 1 \\ \therefore D_2=\frac{10\times 24}{30}=8 days \end{gathered}$$

 Hence, option A is the correct.