$\begin{array}{l}\text{Here,}\\ \\ \Rightarrow 64.5\%of800+36.4\%of1500={(?)}^2+38\\ \\ \Rightarrow \frac{64.5}{100}\times 800+\frac{36.4}{100}\times 1500={(?)}^2+38\\ \\ \Rightarrow \text{64.5}\times \text{8 + 36.4}\times \text{15 = }{(?)}^{\text{2}}+38\\ \\ \Rightarrow {\text{516 + 546 = (?)}}^{\text{2}}+38\\ \\ \Rightarrow {\text{?}}^{\text{2}}\text{= 516+ 546}-\text{38 = 1062}-38\\ \\ \Rightarrow ?=\sqrt{1024}=32\end{array}$

Hence, Option A is correct.