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.
