Multiple choice

The simple interest on a certain sum for 1 year at the rate of 4% p.a. is Rs. 140 less than the simple interest on the same sum for 1.5 years at the rate of 5% p.a. Find the sum.

  1. Rs. 3500

  2. Rs. 2500

  3. Rs. 3000

  4. Rs. 4000

  5. None of these
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D Correct answer
Explanation

Let the sum be P. Interest 1 = P * 0.04 * 1 = 0.04P. Interest 2 = P * 0.05 * 1.5 = 0.075P. The difference is 0.075P - 0.04P = 0.035P = 140. Thus P = 140 / 0.035 = 4000.

AI explanation

The difference in interest is calculated by subtracting the first interest expression from the second, so the principal multiplied by 5 multiplied by 1.5 divided by 100 minus the principal multiplied by 4 multiplied by 1 divided by 100 equals 140. This simplifies to the principal multiplied by 7.5 divided by 100 minus the principal multiplied by 4 divided by 100, which equals the principal multiplied by 3.5 divided by 100. Solving for the principal gives 14000 divided by 3.5, resulting in a sum of Rs. 4,000.

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