**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?**

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6 men complete one task in 24 days.

â€‹\( \therefore \)â€‹ workdone by 6 men in one day is â€‹\( \frac{1}{24} \)â€‹Â .

â€‹\( \therefore \)â€‹ workdone by 1 man in one day is â€‹\( \frac{1}{144} \)â€‹.Â

â€‹\( \therefore \)â€‹ workdone by 7 men in one day will be â€‹\( \frac{7}{144} \)â€‹.Â

Similarly,

8 children complete same task in 24 days.

â€‹\( \therefore \)â€‹ workdone by 8 children in one day is â€‹\( \frac{1}{24} \)â€‹.Â

â€‹\( \therefore \)â€‹ workdone by 1 child in one day is â€‹\( \frac{1}{192} \)â€‹.

â€‹\( \therefore \)â€‹ workdone by 12 children in one day is â€‹\( \frac{12}{192}=\frac{1}{16} \)â€‹.Â

â€‹\( \therefore \)â€‹ workdone by 8 men and 12 children in one day is â€‹\( \frac{7}{144}+\frac{1}{16}=\frac{7}{144}+\frac{9}{144}=\frac{16}{144}=\frac{1}{9} \)â€‹.Â

â€‹\( \therefore \)â€‹Â 9 days will be required to complete the task for 7 men and 12 children.Â

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