| 2 men and 3 women can do a piece of work in 10 days, while 3 men and 2 women can do the same work in 8 days. Then, 2 men and 1 woman can do the same work in |
A) \[12\,\,\text{days}\]
B) \[12\frac{1}{2}\,\,\text{days}\]
C) \[13\,\,\text{days}\]
D) \[13\frac{1}{2}\,\text{days}\]
Correct Answer: B
Solution :
| According to the question, |
| Number of days \[({{M}_{1}}+{{W}_{1}})\] |
| = Number of days \[({{M}_{2}}+{{W}_{2}})\] |
| 10 (2 men + 3 women) = 8 (3 men + 2 women) |
| \[\Rightarrow \]20 men + 30 women = 24 men + 16 women |
| \[\Rightarrow \] 4 men =14 women |
| \[\Rightarrow \] 2 men = 7 women |
| \[\therefore \] 2 men + 3 women = 10 women |
| \[\therefore \] 2 men + 1 woman = 8 women |
| By the formula, |
| \[{{M}_{1}}{{D}_{1}}={{M}_{2}}{{D}_{2}}\] |
| \[\Rightarrow \] \[10\times 10=8\times {{D}_{2}}\] |
| \[\Rightarrow \] \[{{D}_{2}}=\frac{25}{2}=12\frac{1}{2}\text{days}\] |
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