If 6 men or 8 chidren complete one task in 24 days, then how many days will be required to complete the task for 7 men and 12 children?

Question:

If 6 men or 8 chidren complete one task in 24 days, then how many days will be required to complete the task for 7 men and 12 children?

Answer:

6 men complete one task in 24 days.

$\therefore$ workdone by 6 men in one day is $\frac{1}{24}$ .

$\therefore$ workdone by 1 man in one day is $\frac{1}{144}$. 

$\therefore$ workdone by 7 men in one day will be $\frac{7}{144}$. 

Similarly,

8 children complete same task in 24 days.

$\therefore$ workdone by 8 children in one day is $\frac{1}{24}$. 

$\therefore$ workdone by 1 child in one day is $\frac{1}{192}$.

$\therefore$ workdone by 12 children in one day is $\frac{12}{192}=\frac{1}{16}$. 

$\therefore$ workdone by 8 men and 12 children in one day is $\frac{7}{144}+\frac{1}{16}=\frac{7}{144}+\frac{9}{144}=\frac{16}{144}=\frac{1}{9}$. 

$\therefore$ 9 days will be required to complete the task for 7 men and 12 children.