Sandeep borrowed Rupees 3000 for 4 years and rupees 8000 for 2 1/2 years from Sonia at the same rate of interest. The total interest earned by Sonia is Rupees 2880. Find the rate of interest?

Suppose the rate of interest be R.
Now for P = Rs.3000; T = 4 years we have;
Simple interest = $\frac{P\times R\times T}{100} = \frac{3000\times R\times 4}{100}$ = 120R
Also for P = Rs.8000; T = $\frac{5}{2}$ years we have;
Simple interest = $\frac{P\times R\times T}{100} = \frac{8000\times R\times {\displaystyle \frac{5}{2}}}{100} = \frac{8000\times R\times 5}{100\times 2}$ = 200R
Total simple interest = 120R + 200R = Rs.2880
$$\begin{gathered} \Rightarrow 320R = 2880 \\ \Rightarrow R = \frac{2880}{320} = 9 \end{gathered}$$
So, rate of interest is 9% per annum.