20 men complete one-third of a piece of work in 20 days. How many more men should be employed to finish the rest of the work in 25 more days ?

Solution(By Examveda Team)

Let the total number of men be x
Work done = $$\frac{1}{3}$$
Remaining work
= $$\left( {1 - \frac{1}{3}} \right) = \frac{2}{3}$$
More work, More men (Direct proportion)
More days, Less men (Indirect proportion)
\[\left. \begin{gathered} \,{\text{Work }}\frac{1}{3}:\frac{2}{3} \hfill \\ {\text{Days 25}}:20 \hfill \\ \end{gathered} \right\}::20:x\]
$$\eqalign{ & \therefore {\text{ }}\left( {\frac{1}{3} \times 25 \times x} \right) = \left( {\frac{2}{3} \times 20 \times 20} \right) \cr & \Leftrightarrow x = \frac{{800}}{{25}} \cr & \Leftrightarrow x = 32 \cr} $$
∴ More men to be employed = (32 - 20) = 12