(b) 24
1 man’s 1 days’ work = \(\frac{1}{24\times16}\)
\(\therefore\) 16 men’s 1days’ work = \(\frac{16}{24\times16}\) = \(\frac{1}{24}\)
1 woman’s 1 days’ work = \(\frac{1}{32\times24}\)
16 women’s 1 days’ work = \(\frac{16}{32\times24}\) = \(\frac{1}{48}\)
\(\therefore\) 12 days’ work of (16 men + 16 women) = 12\(\big(\frac{1}{24}+\frac{1}{48}\big)\)
= 12\(\big(\frac{2+1}{48}\big)\) = 12 x \(\frac{3}{48}\) = \(\frac{3}{4}\)
Remaining work = 1 - \(\frac{3}{4}\) = \(\frac{1}{4}\)
Now (16 men’s + 16 women’s) 2 days’ work = 2\(\big(\frac{1}{24}+\frac{1}{48}\big)\) = 2 x \(\frac{1}{16}\) = \(\frac{1}{8}\)
\(\therefore\) Remaining work = \(\frac{1}{4}\) - \(\frac{1}{8}\) = \(\frac{1}{8}\)
\(\frac{1}{384}\) work is done in 1 day by 1 man
\(\therefore\) \(\frac{1}{8}\) work will be done in 2 days by \(\big(384\times\frac{1}{8}\times\frac{1}{2}\big)\) = 24 men.