Multiple choice

In the following questions, Quantity I and Quantity II are given. You have to solve both and give answer. $Quantity I: The difference between SI and CI for 2 years is Rs.226.08 and rate of interest is 12%. Then Find the principal invested on CI and SI. \text{Quantity II:} Rs.5000 is invested by Sindhu on CI for 3 years at the rate of 12%. Then find the amount earned by her if sum is compounded half yearly.$

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or the relation cannot be established
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A Correct answer
Explanation

Quantity I: CI - SI for 2 years = P × (r/100)². Given 226.08 = P × (12/100)² = P × 0.0144. So P = 226.08/0.0144 = Rs. 15,700. Quantity II: P = 5000, r = 12%, n = 3 years, compounded half-yearly. A = P(1 + r/200)^(2n) = 5000 × (1 + 12/200)^6 = 5000 × (1.06)^6 ≈ 5000 × 1.4185 = Rs. 7,092.50. Amount earned = Rs. 7,092.50. Since 15,700 > 7,092.50, Quantity I > Quantity II.

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