A sum of money amounts to ₹ 5200 in 5 years and to ₹ 5680 in 7 years at simple interest. The rate of interest per annum is : (S.S.C., 2007)

### Concept & Simple Interest Rate Calculation Once the principal and the interest for a specific period are known, the rate of interest can be calculated using the fundamental simple interest formula. $$Rate = \frac{100 \times S.I.}{Principal \times Time}$$ ### Step-by-Step Solution * Amount in 7 years = ₹ 5680 * Amount in 5 years = ₹ 5200 * S.I. for 2 years ($7 - 5$) = ₹ 5680 - ₹ 5200 = ₹ 480 * S.I. for 1 year = $\frac{480}{2}$ = ₹ 240 * S.I. for 5 years = ₹ 240 × 5 = ₹ 1200 * Principal = Amount in 5 years - S.I. for 5 years = ₹ 5200 - ₹ 1200 = ₹ 4000 * Now, calculate the rate: Rate = $\frac{100 \times 240}{4000 \times 1}$ * Rate = $\frac{24000}{4000}$ = 6% ### Exam Strategy & Shortcut Determine 1-year interest: $\frac{5680 - 5200}{2} = 240$. Find Principal: $5200 - (5 \times 240) = 4000$. Rate percentage is the 1-year interest over Principal: $\frac{240}{4000} \times 100 = 6\%$. ### Common Pitfall Forgetting to calculate the principal first and trying to use the amount directly in the rate formula. ### Final Answer Therefore, the correct answer is **6%**.