$A$, $B$, and $C$ entered into a partnership business by investing $\text{Rs. }64000$, $\text{Rs. }52000$, and $\text{Rs. }36000$ respectively for a certain period of time. If $A$ receives $\text{Rs. }35584$ as annual profit, what amount will $C$ receive as his share in the profit?

The ratio of the investments of $A$, $B$, and $C$ is:
$$A:B:C=64000:52000:36000$$

Dividing each term by $4000$:

$$A:B:C=16:13:9$$

Since the time period is same for all partners, the profit distribution ratio will be identical to the investment ratio.
Let the common multiple be $k$. Thus, $A$ 's share $=16k$.

Given that $A$ 's profit share is $\text{Rs. }35584$:

$$16k=35584$$

$$k=\frac{35584}{16}=2224$$

$C$ 's profit share is $9k$:

$$\text{Profit of }C=9\times 2224=\text{Rs. }20016$$