CAT 2023 Slot 3 Solved Paper

It is given that for some real numbers a and $\mathrm{b}$, the system of equations $\mathit{x}+\mathit{y}=4$ and $\left(\mathit{a}+5\right)\mathit{x}+({\mathit{b}}^2-.$ 15) $\mathit{y}=8\mathit{b}$ has infinitely many solutions for $\mathrm{x}$ and $\mathrm{y}$.
Hence, we can say that
$\Rightarrow \frac{\mathit{a}+5}{1}=\frac{{\mathit{b}}^2-15}{1}=\frac{8\mathit{b}}{4}$
This equation can be used to find the value of $\mathit{a}$, and $\mathit{b}$.
Firstly, we will determine the value of $\mathit{b}$.
$\Rightarrow \frac{{\mathit{b}}^2-15}{1}=\frac{8\mathit{b}}{4}\Rightarrow {\mathit{b}}^2-2\mathit{b}-15=0$
$\Rightarrow \left(\mathit{b}-5\right)\left(\mathit{b}+3\right)=0$
Hence, the values of $\mathit{b}$ are 5 , and -3 , respectively.
The value of a can be expressed in terms of $\mathrm{b}$, which is $\mathit{a}+5={\mathit{b}}^2-15\Rightarrow \mathit{a}={\mathit{b}}^2-20$
When $\mathit{b}=5,\mathit{a}=5^2-20=5$
When $\mathit{b}=-3,\mathit{a}=3^2-20=-11$
The maximum value of $\mathit{a}\mathit{b}=\left(-3\right)\cdot \left(-11\right)=33$
The correct option is A