\(C_{1}=\frac{\varepsilon_{0} A}{3}\)

If a slab of dielectric constant \(K\) is introduced between plates then

\(C=\frac{K \varepsilon_{0} A}{d}\) then \(C'_1 = \frac{{{\varepsilon _0}A}}{{2.4}}\)

\(\mathrm{C}_{1}\) and \({C'}_{1}\) are in series hence,

\(\frac{{{\varepsilon _0}A}}{3} = \frac{{{\text{k}}\frac{{{\varepsilon _0}A}}{3} \cdot \frac{{{\varepsilon _0}A}}{{2.4}}}}{{{\text{k}}\frac{{{\varepsilon _0}A}}{3} + \frac{{{\varepsilon _0}{\text{A}}}}{{2.4}}}}\)

\(3\, k=2.4 \,k+3\)

\(0.6\, \mathrm{k}=3\)

Hence, the dielectric constant of slap is given by, 

\(k=\frac{30}{6}=5\)