The compound interest on $\text{Rs. }10,000$ in $2\frac{1}{2}$ years at $10\%$ per annum is:

The time given is $2\frac{1}{2}$ years. This means interest compounds fully for $2$ years, and for the remaining half-year, the rate is adjusted proportionally to $\frac{1}{2}\times 10\%=5\%$.
The formula for the total accumulated amount $A$ is:

$$A=P\times {\left(1+\frac{R}{100}\right)}^2\times \left(1+\frac{\frac{R}{2}}{100}\right)$$

$$A=10000\times {\left(1+\frac{10}{100}\right)}^2\times \left(1+\frac{5}{100}\right)$$

$$A=10000\times {\left(\frac{11}{10}\right)}^2\times \left(\frac{21}{20}\right)$$

$$A=10000\times \frac{121}{100}\times \frac{21}{20}$$

$$A=5\times 121\times 21=605\times 21=\text{Rs. }12705$$

Now, we calculate the Compound Interest ($\text{CI}$):

$$\text{CI}=A-P=12705-10000=\text{Rs. }2705$$