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$\text{P}$  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 ₹)?

  1. $2500$
  2. $3000$
  3. $4687$
  4. $8437$
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