Assume a man can build the bridge in $x$ weeks and, a woman can build the bridge in $y$ weeks
We get,
- $ \frac{1200}{x} + \frac{500}{y} = \frac{1}{2} \qquad \to (1)$
- $\frac{900}{x} + \frac{250}{y} = \frac{1}{3} \qquad \to(2)$
$2 \times(2) - (1) \implies \frac{600}{x} = \frac{1}{6} \implies x = 3600.$
Hence, Correct Answer is $C.$ 3600 Men