A slab of material of dielectric constant k has the same area as the plates of a parallel plate capacitor, but has a thickness $\frac{3 d}{4}$. Where d is the distance between plates of capaciptor. The ratio of the capacitance with dielectric inside it to its capacitance without the dielectric is:

$\frac{4 k}{(k+3)}$

$ C = \frac{\epsilon_0 A}{d - t +\frac{t}{k}}$

Capacitance without dielectric is $ _ 0 = \frac{\epsilon_0 A}{d}$

Capacitance with dielectric is $ C_1 = \frac{\epsilon_0 A}{d - 3d/4 +\frac{3d/4}{k}} =\frac{\epsilon_0 A}{d/4+\frac{3d/4}{k}} = \frac{4\epsilon_0 A}{d(1+3/k)} = \frac{4k C}{k+3}$

$\frac{C_1}{C_0} = \frac{4k}{k+3}$