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      Question

      Out of Rs. 15,000, 'X' invested a part of it on compound

      interest at 20% p.a. (compounded annually) for 2 years and the remaining amount on simple interest at 15% p.a. for 2 years. If the total interest earned by him was Rs. 5,760, then determine the simple interest earned by him.
      A Rs.1,320 Correct Answer Incorrect Answer
      B Rs.1,800 Correct Answer Incorrect Answer
      C Rs.2,200 Correct Answer Incorrect Answer
      D Rs.3,200 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the amount invested by 'X' on compound interest be Rs. ‘p’. Then, amount invested by 'X' on simple interest = Rs. (15,000 – p) Simple interest = Principal × Rate × Time ÷ 100 Simple interest earned = (15,000 – p) × 15 × 2 ÷ 100 = Rs. (4,500 – 0.3p) Compound interest = Principal × (1 + Rate ÷ 100)² – Principal Compound interest = p × (1.2)² – p ⇒ Compound interest = 1.44p – p = 0.44p ATQ: 0.44p + 4,500 – 0.3p = 5,760 ⇒ 0.14p = 1,260 ⇒ p = 9,000 Amount invested on simple interest = 15,000 – 9,000 = 6,000 Simple interest earned = 6,000 × 0.15 × 2 = Rs.1,800

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