12 men can finish a project in 20 days. 18 women can finish the same project in 16 days and 24 children can finish it in 18 days. 8 women and 16 children worked for 9 days and then left. In how many days will 10 men complete the remaining project ?

12 men can finish the project in 20 days.

=> 1 day work of 1 man = $$\frac{1}{12 \times 20} = \frac{1}{240}$$

Similarly, => 1 day work of 1 woman = $$\frac{1}{18 \times 16} = \frac{1}{288}$$

=> 1 day work of 1 children = $$\frac{1}{24 \times 18} = \frac{1}{432}$$

8 women and 16 children worked for 9 days

=> Work done in 9 days = $$9 \times (8 \times \frac{1}{288}) + (16 \times \frac{1}{432})$$

= $$9 \times (\frac{1}{36} + \frac{1}{27}) = 9 \times \frac{7}{108}$$

= $$\frac{7}{12}$$

=> Work left = $$1 - \frac{7}{12} = \frac{5}{12}$$

$$\therefore$$ Number of days taken by 10 men to complete the remaining work

= $$\frac{\frac{10}{240}}{\frac{5}{12}} = \frac{1}{24} \times \frac{12}{5} = \frac{1}{10}$$

Thus, 10 men will complete the remaining the work in 10 days.