| 6 women and 6 men together can complete a piece of work in 6 days. In how many days can 15 men alone complete the piece of work, if 9 women alone can complete the work in 10 days? |
A) 6
B) 5
C) 7.2
D) Cannot be determined
E) None of the above
Correct Answer: E
Solution :
| Let 1 man's 1 day work be x |
| and 1 woman's 1 day work be y. |
| Then, according to the question, |
| \[6x+6y=\frac{1}{6}\] and \[9y=\frac{1}{10}\] |
| On solving these, we get |
| \[y=\frac{1}{90}\] and |
| \[\Rightarrow \] \[6x=\frac{1}{6}-6y=\frac{1}{6}-\frac{6}{90}\] |
| \[=\frac{1}{6}-\frac{1}{15}=\frac{5-2}{30}=\frac{1}{10}\]\[\Rightarrow \]\[x=\frac{1}{60}\] |
| \[\therefore \] 15 men can finish the work in \[\frac{60}{15}\,=\,\,4days\] |
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