Multiple choice

If the difference between the total compound interest and the total simple interest on a certain sum at a certain rate of interest is ₹1000 at the end of two years and ₹3100 at the end of three years, then find the rate of interest.

  1. 10%

  2. 12.5%

  3. 15%

  4. 20%
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A Correct answer
Explanation

For two years, CI - SI = P(r/100)^2 = 1000. For three years, CI - SI = P(r/100)^2 * (3 + r/100) = 3100. Dividing the second by the first gives 3 + r/100 = 3.1, so r/100 = 0.1, meaning r = 10%.

AI explanation

For any sum and rate, the difference between compound interest and simple interest for three years is given by the formula P * (R/100)^2 * (3 + R/100), and for two years it is P * (R/100)^2. Taking the ratio of the differences, 3100 / 1000 = (3 + R/100). Solving this gives 3.1 = 3 + R/100, so R/100 = 0.1 and the rate of interest is 10%.

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