Correct Answer: $47\frac{3}{19}$

Solution : Given:
15 men and 21 women can do a piece of work in 56 days.
12 men and 24 women can do it in 64 days.
Let the efficiency of 1 man is $x$ and 1 woman's efficiency is $y$.
So, $(15x+21y)×56=(12x+24y)×64$
⇒ $840x+1176y=768x+1536y$
⇒ $72x=360y$
⇒ $\frac{x}{y}=\frac{5}{1}$
Let the total work = $(15×5+21×1)×56=5376$ units.
So, (18 men + 24 women)'s efficiency is $18×5+24×1=114$
Therefore, they will do the work in $\frac{5376}{114}=\frac{896}{19}=47 \frac{3}{19}$ days.
So, 18 men and 24 women working together will finish the job in $47 \frac{3}{19}$ days
Hence, the correct answer is $47 \frac{3}{19}$.