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.
