Multiple choice

Simple interest on a certain sum of money for 4 years at 4 percent per annum lags the compound interest on the same sum for 2 years at 10 percent per annum by Rs. 60. Find the sum.

  1. Rs. 1200

  2. Rs. 1400

  3. Rs. 1500

  4. None of these
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A Correct answer
Explanation

SI = P * 0.04 * 4 = 0.16P. CI = P * (1.1^2 - 1) = 0.21P. Difference = 0.21P - 0.16P = 0.05P = 60. P = 60 / 0.05 = 1200.

AI explanation

Using the simple interest formula SI = (P * R * T) / 100, the interest for 4 years at 4 percent is 0.16P. Using the compound interest formula CI = P[(1 + R/100)^T - 1], the interest for 2 years at 10 percent is P[(1.1)^2 - 1] = 0.21P. Since 0.16P lags 0.21P by Rs. 60, we solve 0.05P = 60 to get P = 1200. The sum is Rs. 1200.

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