Let the weight of the metre scale be ' $\mathit{W}$ ' gf. It will act at the centre of gravity i.e. at $50\mathrm{cm}$ mark.
According to the principle of moments, in equilibrium,
clockwise moment of force $=$ Anticlockwise moment of force
$\mathrm{W}\times \left(50-30\right)=40\times \left(30-5\right)$
$\Rightarrow \mathrm{W}\times 20=40\times 25$
$\Rightarrow \mathrm{W}=\frac{40\times 25}{20}=50\mathrm{gf}$