A) 90 days
B) 60 days
C) 40 days
D) 50 days
Correct Answer: C
Solution :
Work done in 30 days = \[{{W}_{2}}\] \[\therefore \frac{{{M}_{1}}{{D}_{1}}}{{{W}_{1}}}=\frac{{{M}_{2}}{{D}_{2}}}{{{W}_{2}}}\] \[\Rightarrow \] \[\frac{12\times 90}{1}=\frac{12\times 30}{{{W}_{2}}}\] \[\Rightarrow \,\,{{W}_{2}}=\frac{12\times 30}{12\times 90}=\frac{1}{3}\] Remaining work \[=1-\frac{1}{3}=\frac{2}{3}\] New number of men =18 \[\therefore \] \[\frac{{{M}_{1}}{{D}_{1}}}{1}=\frac{{{M}_{2}}{{D}_{2}}}{W}\] \[\Rightarrow \frac{12\times 90}{1}=\frac{18\times {{D}_{2}}}{\frac{2}{3}}\] \[\Rightarrow \,\,18\times {{D}_{2}}=12\times 90\times \frac{2}{3}=12\times 60\] \[\Rightarrow \,\,{{D}_{2}}=\frac{12\times 60}{18}=40\,days\]
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