# 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?

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.