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      Question

      A man invests (10,000 + 100x) rupees at 8% p.a. simple

      interest for 2 years, and (5,000 + 50x) rupees at 6% p.a. simple interest for 3 years. If the total interest from both investments is Rs. 3,000, what is the total principal (sum of both amounts) invested?
      A 12,000 Correct Answer Incorrect Answer
      B 18,000 Correct Answer Incorrect Answer
      C 23,000 Correct Answer Incorrect Answer
      D 29,000 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, First principal: P1 = 10,000 + 100x Rate = 8%, Time = 2 years Interest I1 = P1 × 8 × 2 / 100 = 0.16 P1 I1 = 0.16(10,000 + 100x) = 1,600 + 16x Second principal: P2 = 5,000 + 50x Rate = 6%, Time = 3 years Interest I2 = P2 × 6 × 3 / 100 = 0.18 P2 I2 = 0.18(5,000 + 50x) = 900 + 9x Total interest: I1 + I2 = 3,000 (1,600 + 16x) + (900 + 9x) = 3,000 2,500 + 25x = 3,000 25x = 500 x = 20 Now P1 + P2 = (10,000 + 100×20) + (5,000 + 50×20) = (10,000 + 2,000) + (5,000 + 1,000) = 12,000 + 6,000 = 18,000

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