Correct Answer: 24

Work done = \( \Large \frac{1}{3} \)

Remaining work = \( \Large \left(1-\frac{1}{3}\right)= \left(\frac{3-1}{3}\right)=\frac{2}{3} \)

Let the number of more men to be employed be x.

More work, More men (Direct proportion)

More days, Less men (Indirect proportion)

Work \( \Large \frac{1}{3} \) : \( \Large \frac{2}{3} \)

:: 40 : (40+x)

Days 50 : 40

Therefore,

\( \Large \frac{1}{3} \times 50 \times \left(40+x\right) = \frac{2}{3} \times 40 \times 40 \)

\( \Large 5 \times \left(40+x\right) = 2 \times 40 \times 4 \)

200 + 5x = 320

5x = 320 - 200 = 120

Therefore, x = \( \Large \frac{120}{5} \) = 24

Therefore, Required number of men = 24