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# 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.
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