| 20 men complete one-third of a work in 20 days. How many more men should be employed to finish the rest of the work in 25 more days? |
A) 10
B) 12
C) 15
D) 20
E) None of these
Correct Answer: B
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 more men to be employed be x. |
| More work, more men (Direct proportion) |
| More days, less men (Indirect proportion) |
| \[\left. \begin{align} & \text{Work}\,\,\,\frac{1}{3}:\frac{2}{3} \\ & \text{Days}\,\,25:20 \\ \end{align} \right\}::20:\,\,(20+x)\] |
| \[\therefore \]\[\frac{1}{3}\times 25\times \,\,(20+x)=\frac{2}{3}\times 20\times 20\] |
| \[\Rightarrow \]\[(20+x)=\frac{800}{25}=32\] |
| \[\therefore \] \[x=32-20=12\] |
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