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      Question

      A sum of money is invested at simple interest at (x +

      2)% per annum for 3 years and the interest earned is Rs. 3,000. The same sum invested at x% per annum for 4 years gives an interest of Rs. 3,200. What is the value of x?
      A 10% Correct Answer Incorrect Answer
      B 6% Correct Answer Incorrect Answer
      C 8% Correct Answer Incorrect Answer
      D 4% Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Let principal = P. First case: rate = (x + 2)%, time = 3 years SI₁ = P(x + 2) × 3 / 100 = 3,000 ⇒ P(x + 2) = 3,000 × 100 / 3 = 100,000 … (1) Second case: rate = x%, time = 4 years SI₂ = P x × 4 / 100 = 3,200 ⇒ P x = 3,200 × 100 / 4 = 80,000 … (2) From (1) − (2): P(x + 2) − P x = 100,000 − 80,000 2P = 20,000 P = 10,000 From (2): 10,000 × x = 80,000 ⇒ x = 8

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