For $2X_{\left(k\right)}+Y_{\left(g\right)}\rightleftharpoons 3Q_{\left(g\right)},K_c=50$ at certain temperature, then for $3Q_{\left(g\right)}\rightleftharpoons 2X_{\left(g\right)}+Y_{\left(g\right)},K_p$ equals 

If the reaction is reversed, the value of  $K_c$ is reciprocated. Therefore, the value of $K_c$for the second reaction is $1/50$
$\therefore {\mathrm{K}}_{\mathrm{p}}={\mathrm{K}}_{\mathrm{c}}(\mathrm{RT}{)}^{\Delta \mathrm{n}}$
Here, $(\Delta n=0)\left(K_p=K_c\left(RT\right)°\right)$
$\left(\therefore K_p=K_c=1/50\right)$
Hence the correct answer is C) $\frac{1}{50}$.