Multiple choice

Priya lended a certain amount for 2 years at compound interest on which she recieved Rs. 282.15 as interest. If the simple interest on the same amount is Rs. 12.15 less than its compound interest, then which of the following represents the sum and the rate of interest?

  1. Rs. 500 and 9%

  2. Rs. 1500 and 9%

  3. Rs. 1540 and 11%

  4. Rs. 1900 and 12%

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 2 years, the difference between compound interest (CI) and simple interest (SI) is given by the formula: Difference = P * (r/100)^2. Here, 12.15 = P * (r/100)^2. Also, SI = P * r * 2 / 100 = 282.15 - 12.15 = 270. From SI, P * r = 13500. Substituting P = 13500/r into the difference formula: 12.15 = (13500/r) * (r^2 / 10000) = 1.35 * r. Thus, r = 12.15 / 1.35 = 9%. Then P = 13500 / 9 = 1500.

AI explanation

The difference between compound interest and simple interest for two years is calculated as P * (R/100)^2. Equating this to the given difference of 12.15 gives P * (R/100)^2 = 12.15; testing the provided values of Rs. 1500 and 9% confirms the equation since 1500 * 0.09^2 equals 12.15. The sum is Rs. 1500 and the rate is 9%.

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