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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?

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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. 
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