Explanation:

- To find the rate of interest, we use the formula for simple interest: $\text{SI}=\frac{P\times R\times T}{100}$.

- Combine interests from all deposits:

- For ?500 for 3 years: $\frac{500\times R\times 3}{100}$

- For ?650 for 5 years: $\frac{650\times R\times 5}{100}$

- For ?1,250 for 7 years: $\frac{1250\times R\times 7}{100}$

- Add equations: $\frac{500\times R\times 3}{100}+\frac{650\times R\times 5}{100}+\frac{1250\times R\times 7}{100}=1620$.

- Simplifying gives: $15R+32.5R+87.5R=1620\to 135R=1620$.

- Solving for R yields: $R=12\mathrm{\%}$.

- Correct Answer: Option 1 - 12%.

.