Which among the following denotes the correct relationship between ${\mathrm{K}}_{\mathrm{p}}$ and ${\mathrm{K}}_{\mathrm{c}}$ for the reaction $2{\mathrm{A}}_{\left(\mathrm{g}\right)}\rightleftharpoons {\mathrm{B}}_{\left(\mathrm{g}\right)}+{\mathrm{C}}_{\left(\mathrm{g}\right)}$

So we know the relation between the equilibrium constant and equilibrium pressure constant 

So the formula is 

${\mathrm{K}}_{\mathrm{P}} = {\mathrm{K}}_{\mathrm{C}}{\left(\mathrm{RT}\right)}^{∆{\mathrm{n}}_{\mathrm{g}}}$

Whereas we know that $∆{\mathrm{n}}_{\mathrm{g}}$ is the difference of the gaseous number of moles of reactant side and product side

$∆{\mathrm{n}}_{\mathrm{g}} = 2-2=0$

Thus, the relation is 

${\mathrm{K}}_{\mathrm{P}} = {\mathrm{K}}_{\mathrm{C}}$