Multiple choice

Ifthe compound interest for 2 years on a certain sum be Rs 63 and the simple interest for 3 years on the same sum at same rate be Rs 90, then the sum will be

  1. Rs 300

  2. Rs 315

  3. Rs 325

  4. Rs 350
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A Correct answer
Explanation

The simple interest for 3 years gives 3Pr = 90, so Pr = 30. The two-year compound interest is 2Pr + Pr^2 = 63, giving Pr^2 = 3 and r = 0.1. Therefore, P = 30/0.1 = Rs 300.

AI explanation

Using the relationship between simple and compound interest, the simple interest for one year is 90 / 3 = 30, making the simple interest for two years equal to 60. The difference between the compound interest and simple interest for two years is 63 - 60 = 3, which represents the interest earned on the first year's interest. This means the rate is 3 / 60 = 5%, and dividing the one-year simple interest of 30 by 0.05 gives the principal. The sum is Rs 300.

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