Simple interest accrued on a certain sum is 16/25 of the principal sum. If the numerical value of the rate of annual interest (%) and time (years) are equal, what is annual rate of interest?

Correct option is D

​$$\text{Given: Simple Interest (SI)} = \frac{16}{25} \times P \\[10pt]\text{Let the Principal be } P \\[10pt]\text{Also, SI} = \frac{P \times R \times T}{100} \\[10pt]\text{Given: } R = T \\[10pt]\Rightarrow \text{SI} = \frac{P \times R^2}{100} \\[10pt]\text{Now equating both expressions for SI:} \\\frac{P \times R^2}{100} = \frac{16}{25} \times P \\[10pt]\text{Cancelling } P \text{ from both sides:} \\\frac{R^2}{100} = \frac{16}{25} \\[10pt]R^2 = \frac{16}{25} \times 100 = \frac{1600}{25} = 64 \\[10pt]R = \sqrt{64} = 8 \\[10pt]\text{Therefore, the annual rate of interest is } {8\%}$$​​