CAT 2023 Slot 1 Solved Paper

Given that $\mathit{A}\mathit{B}\mathit{C}$ is a right-angled triangle with $\mathit{A}\mathit{B}=5$ and $\mathit{B}\mathit{C}=12\Rightarrow$ Area of the triangle $=0.5*5*12=30$.
Let us assume $\mathit{B}\mathit{P}=\mathit{p},\mathit{B}\mathit{Q}=\mathit{q}$
$\Rightarrow$ Area of $\mathit{A}\mathit{B}\mathit{P}=0.5*5*\mathit{p}=2.5\mathit{p}$
$\Rightarrow$ Area of $\mathit{A}\mathit{B}\mathit{Q}=0.5*5*\mathit{q}=2.5\mathit{q}$
Given the area of $\mathit{A}\mathit{B}\mathit{C}$ is 1.5 times that of $\mathit{A}\mathit{B}\mathit{P}$
$\Rightarrow 30=1.5*2.5\mathit{p}\Rightarrow 20=2.5\mathit{p}\Rightarrow \mathit{p}=8$
Given Areas of $\mathit{A}\mathit{B}\mathit{P},\mathit{A}\mathit{B}\mathit{Q}$ and $\mathit{A}\mathit{B}\mathit{C}$ are in A.P. $\Rightarrow 2*2.5\mathit{q}=2.5*8+30\Rightarrow 5\mathit{q}=50\Rightarrow \mathit{q}=10$.
$\mathit{P}\mathit{Q}=\mathit{B}\mathit{Q}-\mathit{B}\mathit{P}=\mathit{q}-\mathit{p}=10-8=2.$