$\text{P}$ invested ₹$5000$ per month for $6$ months of a year and $\text{Q}$ invested ₹$x$ per month for $8$ months of the year in a partnership business. The profit is shared in proportion to the total investment made in that year.
If at the end of that investment year, $\text{Q}$ receives $\frac{4}{9}$ of the total profit, what is the value of $x$ (in ₹)?
- $2500$
- $3000$
- $4687$
- $8437$