Equilibrium: JEE Main 2023 Chemistry question

A litre of buffer solution contains 0.1 mole of each of NH$_3$ and NH$_4$Cl. On the addition of 0.02 mole of HCl by dissolving gaseous HCl, the pH of the solution is found to be _____________ $\times$ 10$^{-3}$ (Nearest integer) [Given : $\mathrm{pK_b(NH_3)=4.745}$ $\mathrm{\log2=0.301}$ $\mathrm{\log3=0.477}$ $\mathrm{T=298~K]}$