A sum of Rs. 725 is lent in beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at rate twice former. At end of year, Rs. 33.50 is earned as interest from both loans. What was original rate of interest?

Let the original rate be R%. Then, new rate = (2R)%.
Note:
Here, original rate is for 1 year(s); the new rate is for only 4 months i.e. $$\frac{1}{3}$$ year(s).
$$\eqalign{ & \therefore {\frac{{725 \times R \times 1}}{{100}}} + {\frac{{362.50 \times 2R \times 1}}{{100 \times 3}}} \cr & = 33.50 \cr & \Rightarrow \left( {2175 + 725} \right)R = 33.50 \times 100 \times 3 \cr & \Rightarrow \left( {2175 + 725} \right)R = 10050 \cr & \Rightarrow \left( {2900} \right)R = 10050 \cr & \Rightarrow R = \frac{{10050}}{{2900}} = 3.46 \cr & \therefore \text{Original rate} = 3.46\% \cr} $$