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 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 ?
1). $$10\frac{1}{2}$$
2). 10
3). 9
4). $$11\frac{1}{2}$$
1 answers
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.