1. **State the problem:** We need to find the difference between simple interest (SI) and compound interest (CI) on Rs. 1200 for one year at an interest rate of 10% per annum, with compounding done half-yearly. 2. **Calculate Simple Interest (SI):** The formula for simple interest is: $$ SI = \frac{P \times R \times T}{100} $$ Where: - $P = 1200$ (principal) - $R = 10$ (rate per annum) - $T = 1$ year So, $$ SI = \frac{1200 \times 10 \times 1}{100} = 120 $$ 3. **Calculate Compound Interest (CI):** Since the interest is compounded half-yearly, the rate per half year is: $$ \frac{10}{2} = 5\% $$ The number of half-year periods in 1 year is: $$ 2 \times 1 = 2 $$ The compound amount is given by: $$ A = P \left(1 + \frac{r}{100}\right)^n = 1200 \left(1 + \frac{5}{100} \right)^2 = 1200 \times (1.05)^2 $$ Calculate: $$ 1.05^2 = 1.1025 $$ So, $$ A = 1200 \times 1.1025 = 1323 $$ Hence, compound interest is: $$ CI = A - P = 1323 - 1200 = 123 $$ 4. **Find the difference between CI and SI:** $$ CI - SI = 123 - 120 = 3 $$ **Final answer:** The difference is Rs. 3. Hence, the correct option is **b) Rs. 3**.