At which sum the simple interest at the rate of $3 \frac{3}{4}$% per annum will be ₹ 210 in $2 \frac{1}{3}$ years?

### Concept & Fractional Rates and Time When the rate and time are given as mixed fractions, convert them to improper fractions before substituting them into the Principal formula: $$P = \frac{SI \times 100}{R \times T}$$ ### Step-by-Step Solution * Given Simple Interest, $SI = \text{₹ } 210$ * Convert Rate to an improper fraction: $R = 3 \frac{3}{4}\% = \frac{15}{4}\%$ p.a. * Convert Time to an improper fraction: $T = 2 \frac{1}{3} \text{ years} = \frac{7}{3} \text{ years}$ * Substitute values into the formula: $P = \frac{210 \times 100}{(\frac{15}{4}) \times (\frac{7}{3})}$ $P = \frac{210 \times 100 \times 4 \times 3}{15 \times 7}$ * Simplify the expression: $15 \times 7 = 105$ $P = \frac{210}{105} \times 1200$ $P = 2 \times 1200 = \text{₹ } 2400$ ### Exam Strategy & Shortcut Multiply the fractional denominators first and bring them to the numerator: $R \times T = (\frac{15}{4}) \times (\frac{7}{3}) = \frac{105}{12}$. Now calculate $P = 210 \times \frac{12}{105} \times 100$. Since $210$ is exactly double $105$, this immediately simplifies to $2 \times 12 \times 100 = 2400$. ### Common Pitfall Students often try converting fractions like $\frac{7}{3}$ to decimals ($2.33...$), causing compounding rounding errors. Stick to fractions. ### Final Answer Therefore, the correct answer is **₹ 2400**.