A sum of money at simple interest amounts to ₹ 815 in 3 years and to ₹ 854 in 4 years. The sum is

### Concept & Simple Interest Simple interest is constant for each year. By finding the difference between the amounts for different time periods, we can find the interest for the intervening period. $$Amount = Principal + Simple Interest$$ ### Step-by-Step Solution * Amount in 4 years = Principal + S.I. for 4 years = ₹ 854 * Amount in 3 years = Principal + S.I. for 3 years = ₹ 815 * Subtracting the two equations gives S.I. for 1 year = ₹ 854 - ₹ 815 = ₹ 39 * Now, calculate the S.I. for 3 years: ₹ 39 × 3 = ₹ 117 * Principal (Sum) = Amount in 3 years - S.I. for 3 years * Principal = ₹ 815 - ₹ 117 = ₹ 698 ### Exam Strategy & Shortcut Find the 1-year interest directly by subtracting the amounts ($854 - 815 = 39$). Then subtract 3 years of interest from the 3-year amount: $815 - (3 \times 39) = 698$. ### Common Pitfall Mistakenly using the amount as the principal or calculating the interest for the wrong number of base years. ### Final Answer Therefore, the correct answer is **₹ 698**.