\(\frac{m_1d_1}{w_1} = \frac{m_2d_2}{w_2}\)

\(\frac{20*20}{(1/3)}=\frac{(x+20)*25}{(2/3)}\)

\(\frac{20*20}{1}=\frac{(x+20)*25}{2}\)

\(\frac{20*20*2}{25}=x+20\)

\(8*4=32=x+20\)

\(x=32-20=12\)

Work = number of workers * rate * time

So for 20 workers, 20 days with 1/3 of the job done, we solve for the rate. This gives us 1/1200 which represents the amount of work done by ONE man in ONE day. This rate will be the same regardless of the extra men hired.

(2/3) = (x+20) * (1/1200) * (25)

We use 25 for the extra days remaining and 2/3 for the rest of the work left. x represents the extra people needed to be hired on top of the 20 that are already working. From here we solve for x, and see that x=12. Option B.