Multiple choice

Mr. Sam invested 1/6th of a certain sum at 6% per annum for two years and 3/5th of the sum at 8% per annum for two years and the remaining sum at 10% per annum for two years simple interest. If the total simple interest received is Rs. 6002.4, then what was the total sum invested by Mr. Sam?

  1. Rs. 36,900

  2. Rs. 35,900

  3. Rs. 32,900

  4. Rs. 34,900

  5. None of these
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A Correct answer
AI explanation

Let the total sum be P; the fractions invested are 1/6, 3/5, and 7/30, all for 2 years. The total simple interest is Rs. 6002.4, so using the simple interest formula we write 6002.4 = P * 2 * [ (1/6 * 0.06) + (3/5 * 0.08) + (7/30 * 0.10) ]. This simplifies to 6002.4 = P * 2 * (0.01 + 0.048 + 0.02333), or 6002.4 = 0.16266P. Solving for P gives P = 36900, meaning the total sum invested was Rs. 36,900.

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