12 men can finish a project in 20 days. 18 women can finish the same p

1.	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). 103). 94). $$11\frac{1}{2}$$
Answer» Solution 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.

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). 103). 94). $$11\frac{1}{2}$$

Answer»

Solution

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.