The distance between two plates of a capacitor is d and its capacitance is C 1 , when air is the medium…

The formula of capacitance is $C_1=\left(\frac{{\epsilon }_{0}A}{d}\right)$

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

The new value of capacitance is 

$C_2=\frac{{\epsilon }_{0}A}{d-t+{\displaystyle \frac{t}{K_{metal}}}}=\frac{{\epsilon }_{0}A}{d-{\displaystyle \frac{2d}{3}}+{\displaystyle 0}}=3C_1$

Clearly, the ratio,

$\frac{C_2}{C_1}=\frac{3C_1}{C_1}=3:1$