Multiple choice

The compounded interest and the simple interest for 2 years on a certain sum at a certain interest rate are Rs. 8280 and Rs. 7200, respectively. Find the principal (is Rs.) and interest rate.

  1. P = 12,000, R = 30%

  2. P = 13,000, R = 20%

  3. P = 12,000, R = 25%

  4. P = 10,000, R = 35%

  5. P = 15,000, R = 35%
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A Correct answer
Explanation

For 2 years, Simple Interest (SI) = 2*P*R = 7200, so PR = 3600. Compound Interest (CI) = P((1+R)^2 - 1) = P(2R + R^2) = 2PR + PR^2 = 8280. Substituting 2PR = 7200, we get 7200 + PR^2 = 8280, so PR^2 = 1080. Dividing PR^2 by PR gives R = 1080/3600 = 0.3 or 30%. Then P = 3600/0.3 = 12,000.

AI explanation

The difference between compound interest and simple interest for two years is Rs. 1080, which equals P * (R / 100)^2; since the simple interest for two years is Rs. 7200, P * R equals 360000. Solving these two equations yields R = 30 percent and P = Rs. 12000.

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