Question
Consider only numeric value. Quantity I: A sum of
money becomes ₹6,000 in 4 years and ₹7,200 in 5 years at simple interest. Find the rate of interest per annum. Quantity II: A person invested ₹20,000 in a scheme offering 8% compound interest per annum, compounded annually. Find the amount he will receive after 2 years. Quantity III: A certain sum of money amounts to ₹15,000 in 3 years at 10% per annum on simple interest. Find the principal amount.Solution
Quantity I: Difference in amount after 1 year = ₹7,200 - ₹6,000 = ₹1,200. This difference represents 1 year of simple interest, so the interest per year is ₹1,200. Since this is simple interest, we calculate the rate as follows: Rate per annum = (1,200 / 6,000) * 100 = 20%. Quantity II: Using the compound interest formula: Amount = Principal * (1 + Rate / 100) ^ Time. Amount = 20,000 * (1 + 8/100)^2. Amount = 20,000 * (1.08)^2. Amount = 20,000 * 1.1664 = ₹23,328. Quantity III: Using the simple interest formula: Amount = Principal + (Principal * Rate * Time) / 100. 15,000 = Principal + (Principal * 10 * 3) / 100. 15,000 = Principal (1 + 0.3) = Principal * 1.3. Principal = 15,000 / 1.3 ≈ ₹11,538.5 Comparing the quantities: Quantity I = 20%, Quantity II = 23,328, Quantity III = 11,538. Answer: (B) Quantity I < Quantity III > Quantity II
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