Chemistry Question from JEE Main 2025 · 7 April, Shift 2

One litre buffer solution was prepared by adding $0.10 \, \text{mol}$ each of $NH_3$ and $NH_4Cl$ in deionised water. The change in pH on addition of $0.05 \, \text{mol}$ of $HCl$ to the above solution is _____ $\times 10^{-2}$, (Nearest integer) (Given : $pK_b$ of $NH_3 = 4.745$ and $\log_{10}3 = 0.477$)