Description for Correct answer:
1 man can finish the work in \( \Large 8 \times 12 \) = 96 days

1 woman can finish the work in \( \Large 4 \times 48 \) = 1 92 days

1 child can finish the work in \( \Large 10 \times 24 \) = 240 days

1 man's 1 day's work = \( \Large \frac{1}{96} \)

1 woman's 1 day's work = \( \Large \frac{1}{192} \)

1 child's 1 day's work = \( \Large \frac{1}{240} \)

(10 men + 4 women + 10 children)'s 1 day's work

= \( \Large \left(\frac{10}{96}+\frac{4}{192}+\frac{10}{240}\right) \)

= \( \Large \left(\frac{5}{48}+\frac{1}{48}+\frac{1}{24}\right) \)

=\( \Large \left(\frac{5+1+2}{48}\right) \)

= \( \Large \frac{8}{48} = \frac{1}{6} \)

Hence, they will finish the work in 6 days.