According to the question the metre scale having a weight of $50\mathrm{gf}$ is balanced at 40 $\mathrm{cm}$ mark without any weight suspended on it. So, its weight acts at $40\mathrm{cm}$ mark which is also the centre of gravity of this non-uniform metre scale.
Thus, $0\mathrm{cm}$ to $40\mathrm{cm}$ length will have a weight of $25\mathrm{gf}$
And, $40\mathrm{cm}$ to $100\mathrm{cm}$ length will have a weight of $25\mathrm{gf}$.
Thus, if we cut this ruler from $50\mathrm{cm}$ mark (i.e. centre), the part 0 to $50\mathrm{cm}$ part of the ruler will weigh more than $25\mathrm{gf}$.