Multiple choice

The simple interest on a certain sum of money for 4 years at 4% per annum exceeds the compound interest on the same sum for 3 years at 5% per annum by Rs. 228. Find the sum.

  1. Rs. 96,000

  2. Rs. 91,000

  3. Rs. 86,000

  4. Rs. 81,000

  5. Rs. 80,000
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A Correct answer
Explanation

Let the sum be P. Simple interest = P * 0.04 * 4 = 0.16P. Compound interest = P * (1 + 0.05)^3 - P = P * (1.157625 - 1) = 0.157625P. The difference is 0.16P - 0.157625P = 0.002375P = 228. Solving for P gives P = 228 / 0.002375 = 96,000.

AI explanation

Let the sum be P. The simple interest formula gives the first interest as (P * 4 * 4) / 100 = 0.16P. The compound interest for 3 years at 5% is P * (1 + 5/100)^3 - P = P * (1.157625 - 1) = 0.157625P. Setting the difference to 228 gives 0.16P - 0.157625P = 228, so 0.002375P = 228. Solving this yields P = 96000, which is Rs. 96,000.

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