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 ?

Answer: Option B

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)
$$\begin{array}{c}\text{Work }\frac{1}{3}:\frac{2}{3}\text{hfill}\\ \text{Days 25}:20\text{hfill}\end{array}\}::20:x$$
$$\begin{array}{rl}& \therefore \left(\frac{1}{3}\times 25\times x\right)=\left(\frac{2}{3}\times 20\times 20\right)\\ & \iff x=\frac{800}{25}\\ & \iff x=32\end{array}$$
∴ More men to be employed = (32 - 20) = 12