Barun invests $\text{Rs. }5000$ for a year and Tarun joins him with $\text{Rs. }8000$ after six months. After the year they receive a return of $\text{Rs. }4500$, then Tarun's share is:

The profit-sharing ratio in a partnership is determined by the product of the capital investment amount and the time duration for which it was invested.
* Barun's investment duration $=12\text{ months}$
* Tarun's investment duration $=12-6=6\text{ months}$

Let's compute the ratio of profit shares (Barun : Tarun):

$$\text{Ratio}=(5000\times 12):(8000\times 6)$$

$$\text{Ratio}=60000:48000$$

$$\text{Ratio}=60:48=5:4$$

The total return profit is $\text{Rs. }4500$.

$$\text{Tarun’s share}=\frac{4}{5+4}\times 4500$$

$$\text{Tarun’s share}=\frac{4}{9}\times 4500=4\times 500=\text{Rs. }2000$$

Thus, Tarun's share is $\text{Rs. }2000$.