| 40 men complete one-third of a work in 40 days. How many more men should be employed to finish the rest of the work in 50 more days? |
A) 12
B) 20
C) 18
D) 24
E) None of these
Correct Answer: D
Solution :
| Work done \[=\frac{1}{3}\] |
| Remaining work \[=\left( 1-\frac{1}{3} \right)=\left( \frac{3-1}{3} \right)=\frac{2}{3}\] |
| Let the number of additional men be x. |
| More work, More men [direct proportion] |
| More days, Less men [indirect proportion] |
| \[\left. \begin{align} & \text{Work}\,\,\frac{\text{1}}{\text{3}}\text{:}\frac{\text{2}}{\text{3}} \\ & \text{Days}\,\,50:40 \\ \end{align} \right\}::40:(40+x)\] |
| \[\therefore \] \[\frac{1}{3}\times 50\times (40+x)=\frac{2}{3}\times 40\times 40\] |
| \[\Rightarrow \] \[5\times (40+x)=2\times 40\times 4\] |
| \[\Rightarrow \] \[200+5x=320\] |
| \[\Rightarrow \] \[5x=320-200=120\] |
| \[\Rightarrow \] \[x=\frac{120}{5}=24\] |
| \[\therefore \]Required number of men \[=24\] |
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