We know that, ${\color{Green}{\boxed{\text{Profit} = \text{Investment} \times \text{Time}}}}$
Let the total profit be ₹ $k.$
- Profit received by $\text{Q} =$ ₹$\;\frac{4}{9}k$
- Profit received by $\text{P} = k – \frac{4}{9}k =$ ₹$\;\frac{5}{9}k$
Now, $\dfrac{\text{Profit}_{\text{P}}}{\text{Profit}_{\text{Q}}} = \dfrac{\text{Investment}_{\text{P}} \times \text{Time}_{\text{P}}}{\text{Investment}_{\text{Q}}\times \text{Time}_{\text{Q}}}$
$\Rightarrow \dfrac{\frac{5k}{9}}{\frac{4k}{9}} = \dfrac{5000 \times 6}{x \times 8}$
$\Rightarrow \dfrac{5}{4} = \dfrac{5000 \times 3}{4x }$
$\Rightarrow 5x = 15000$
$\Rightarrow {\color{Blue}{\boxed{x = 3000}}}$
$\therefore$ The value of $x =$ ₹$\;3000.$
Correct Answer $:\text{B}$