At the rate of $8\frac{1}{2}\%$ p.a. simple interest, a sum of ₹ 4800 will earn how much interest in 2 years 3 months?

### Concept & Formula Convert fractional percentages and mixed time units into improper fractions to simplify calculation in the Simple Interest formula. $$SI = \frac{P \times R \times T}{100}$$ ### Step-by-Step Solution * **Given:** * Principal ($P$) = ₹ 4800 * Rate ($R$) = $8\frac{1}{2}\%$ = $\frac{17}{2}\%$ p.a. * Time ($T$) = 2 years 3 months = $2 + \frac{3}{12}$ years = $2 + \frac{1}{4}$ years = $\frac{9}{4}$ years. * **Calculation:** * $SI = \frac{4800 \times (\frac{17}{2}) \times (\frac{9}{4})}{100}$ * $SI = 48 \times \frac{17}{2} \times \frac{9}{4}$ * $SI = \frac{48 \times 153}{8}$ * $SI = 6 \times 153$ * $SI = 918$ ### Exam Strategy & Shortcut Cancel denominators early. The denominators in the rate (2) and time (4) multiply to 8. You can quickly divide $4800$ by $100 \times 8 = 800$. $4800 / 800 = 6$. Then multiply by the numerators: $6 \times 17 \times 9 = 102 \times 9 = 918$. ### Common Pitfall Using 2.3 for "2 years 3 months" instead of converting 3 months to $\frac{3}{12}$ or $0.25$ of a year. ### Final Answer Therefore, the correct answer is **₹ 918**.