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      Question

      Two quantities are

      given as Quantity I and Quantity II. You have to determine the relationship between them and give the answer. Ms. Anika invests in two schemes on compound interest: Scheme A at 5% p.a. and Scheme B at 15% p.a., both compounded annually. The total investment across both schemes is Rs.20000. After 2 years, the total interest earned is Rs.4690. Quantity I: Amount invested in Scheme A. Quantity II: Amount invested in Scheme B.
      A Quantity I > Quantity II Correct Answer Incorrect Answer
      B Quantity I < Quantity II Correct Answer Incorrect Answer
      C Quantity I = Quantity II or Relation cannot be established Correct Answer Incorrect Answer
      D Quantity I ≥ Quantity II Correct Answer Incorrect Answer
      E Quantity I ≤ Quantity II Correct Answer Incorrect Answer

      Solution

      ATQ, Let x be the amount invested in Scheme A and (20000 − x) be the amount invested in Scheme B. For 2 years, compound interest ⇒ Scheme A, Net effective interest ⇒ 5 + 5 + (5×5/100) = 10.25% Scheme B, Net effective interest ⇒ 15 + 15 + (15×15/100) = 32.25% 10.25/100 × x + 32.25/100 × (20000 − x) = 4690 (0.1025 − 0.3225)x = 4690 − 0.3225×20000 −0.2200x = 4690 − 6450 = −1760 x = (−1760)/(−0.22) = 8000 Therefore, Quantity I = 8000 and Quantity II = 20000 − 8000 = 12000 Conclusion: Quantity I < Quantity II.

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