Given that, the average of the monthly salaries of $\text{M, N},$ and $\text{S}$ is $₹\;4000.$

$\Rightarrow \frac{\text{M + N + S}}{3} = 4000$

$\Rightarrow\text{M + N + S} = 12000 \quad \longrightarrow (1)$

Also, the average of the monthly salaries of $\text{N, S},$ and $\text{P}$ is $₹\;5000.$

$\Rightarrow \frac{\text{N + S + P}}{3} = 5000$

$\Rightarrow \text{N + S + 6000} = 15000 \quad [{\color{Blue}{\because \text{P} = ₹\;6000}}]$

$\Rightarrow \text{N + S} = 9000 \quad \longrightarrow (2)$

Solving the equation $(1)\; \& \;(2),$ we get ${\color{Green}{\text{M} = ₹\;3000}}.$

$\therefore$ The monthly salary of $\text{M}$ as a percentage of the monthly salary of $\text{P} = \left(\frac{3000}{6000} \right) \times 100\% = 50\%.$

Correct Answer $:\text{A}$