| 8 men can complete a work in 12 days, 4 women can complete it in 48 days and 10 children can complete the same work in 24 days. In how many days can 10 men, 4 women and 10 children complete the same work? |
A) 10
B) 5
C) 7
D) 6
E) None of these
Correct Answer: D
Solution :
| 1 man can finish the work in \[(8\times 12)=96\,\,\text{days}\] |
| 1 woman can finish the work in \[(4\times 48)=192\,\,\text{days}\] |
| 1 child can finish the work in\[(10\times 24)=240\,\,\text{days}\] |
| 1 man's 1 day's work \[=\frac{1}{96}\] |
| 1 woman's 1 day's work \[=\frac{1}{192}\] |
| 1 child's 1 day's work \[=\frac{1}{240}\] |
| (10 men + 4 women + 10 children)'s 1 day's work |
| \[=\left( \frac{10}{96}+\frac{4}{192}+\frac{10}{240} \right)=\left( \frac{5}{48}+\frac{1}{48}+\frac{1}{24} \right)\] |
| \[=\left( \frac{5+1+2}{48} \right)=\frac{8}{48}=\frac{1}{6}\] |
| Hence, they will finish the work in 6 days. |
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