Multiple choice

Ravi lends a certain sum of money at simple interest and compound interest. The ratio of the difference between compound interest and simple interest for 3 years to that for 2 years is 25 : 8. What is the rate of interest per annum?

  1. 12.5%

  2. 10.5%

  3. 8.5%

  4. 6.5%

  5. None of these
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A Correct answer
Explanation

The difference between CI and SI for 2 years is P(r/100)^2. For 3 years, it is P(r/100)^2 * (3 + r/100). The ratio of these differences is 1 : (3 + r/100). Given the ratio is 8 : 25, we have 8 / 25 = 1 / (3 + r/100). Thus, 3 + r/100 = 25/8 = 3.125, so r/100 = 0.125, which means r = 12.5%.

AI explanation

Using the formulas for the difference between compound and simple interest for 2 and 3 years, the ratio is R plus 100 divided by 100, which equals 25 divided by 8. Solving for R, we have 8R plus 800 equals 2500. This yields 8R equals 1700, meaning the rate of interest is 12.5 percent.

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