If the interest on a sum of Rs.1200 is more than the interest on Rs.1000 by Rs.120 in three years, than find the rate of interest per annum.

Correct option is A

​$$\text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \\[5pt]\text{Where:} \\\quad - P \text{ is the principal amount} \\\quad - R \text{ is the rate of interest per annum} \\\quad - T \text{ is the time in years} \\[10pt]\text{Step 1: Let the rate of interest be } R\% \text{ per annum.} \\[5pt]\text{The interest on Rs.1200 for 3 years will be:} \\\text{Interest on } 1200 = \frac{1200 \times R \times 3}{100} = \frac{3600R}{100} = 36R \\[10pt]\text{The interest on Rs.1000 for 3 years will be:} \\\text{Interest on } 1000 = \frac{1000 \times R \times 3}{100} = \frac{3000R}{100} = 30R \\[10pt]\text{According to the given information, the difference in interest is Rs.120, so:} \\36R - 30R = 120 \\6R = 120 \\R = \frac{120}{6} = 20$$​​