The distance between two plates of a capacitor is d and its...

The formula of capacitance is ${C}_{1} = \left(\dfrac{{ε}_{0}A}{d}\right)$

The dielectric constant of metal sheet is ${K}_{metal} = \infty$

The new value of capacitance is

${C}_{2} = \dfrac{{ε}_{0}A}{d - t + \dfrac{t}{{K}_{metal}}} = \dfrac{{ε}_{0}A}{d - \dfrac{2d}{3} + 0} = 3{C}_{1}$

Clearly, the ratio,

$\dfrac{{C}_{2}}{{C}_{1}} = \dfrac{3{C}_{1}}{{C}_{1}} = 3: 1$