Multiple choice

Sanjana invested Rs. 15000 in SI at the rate of 2x% per annum for two years and the same amount is invested in CI at the same rate of interest if she received Rs.150 more interest than S.I, then find the rate of interest per annum?

  1. 10 %

  2. 14 %

  3. 12 %

  4. 16 %

  5. None of these
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A Correct answer
Explanation

Simple Interest (SI) = P * (2x/100) * 2 = 0.04Px. Compound Interest (CI) = P * (1 + 2x/100)^2 - P = P * (4x/100 + 4x^2/10000). The difference is CI - SI = P * (4x^2/10000) = 150. With P = 15000, 15000 * 4x^2 / 10000 = 150, so 6x^2 = 150, x^2 = 25, x = 5. The rate is 2x = 10%.

AI explanation

The simple interest is 15000 multiplied by 2x multiplied by 2 divided by 100, which equals 600x. The compound interest is 15000 multiplied by the quantity 1 plus 2x divided by 100 squared, minus 15000. Equating the difference of compound interest and simple interest to 150 gives 6x squared equals 150. Solving for x gives x equals 5, so the rate per annum is 2x, which is 10 percent.

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