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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.
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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