Question
A person invests a sum of money in two schemes, P and Q.
Scheme P offers simple interest, and Scheme Q offers compound interest. The amount invested in each scheme and their rates of interest are unknown. What is the total interest earned from both schemes after 2 years? Statements: 1. The amount invested in Scheme Q is ₹5,000, and it compounds annually at 10% per annum. 2. The amount invested in Scheme P is double the amount in Scheme Q and earns simple interest at a rate of 12% per annum.Solution
From Statement 1: Investment in Scheme Q = ₹5,000 at 10% compound interest. Using the compound interest formula, Amount after 2 years = 5000 * (1 + 10/100) ²  = 5000 * 1.21 = ₹6,050. Interest from Scheme Q = 6050 - 5000 = ₹1,050. Statement 1 alone does not provide the interest from Scheme P. From Statement 2: Investment in Scheme P is 5000 * 2 = ₹10,000 at 12% simple interest for 2 years. Interest = 10000 * 12 * 2 / 100 = ₹2,400. Statement 2 alone does not provide the interest from Scheme Q. Combining Statements 1 and 2: Total interest = 1050 + 2400 = ₹3,450. Correct Answer: (c) Both statements together are sufficient, but neither alone is sufficient.
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