A monopoly canteen serves packed meals to two groups of consumers, group $X$ and group $Y$. The demand for packed meals for $X$ and $Y$ are given by,
\[
Q_X = 200 - 4P \quad \text{and} \quad Q_Y = 300 - P,
\]
where $P$ is the uniform price per unit. The unit cost of producing each meal is Rs. 50. The value of $P$ (in Rs.) that maximizes the canteen’s profit is