Multiple choice

The simple interest on a certain sum for 14 months at 6 percent per annum is Rs.25 more than the simple interest on the same sum for 8 months at 8 percent. The sum borrowed is -

  1. $Rs.1,500$
  2. $Rs.1,700$
  3. $Rs.2,000$
  4. $Rs.2,500.$
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A Correct answer
Explanation

Let sum be P. Interest 1 = P * 6 * (14/12) / 100 = 84P / 1200 = 0.07P. Interest 2 = P * 8 * (8/12) / 100 = 64P / 1200 = 0.0533P. Difference = 0.07P - 0.0533P = 25. 0.0166P = 25. P = 25 / (20/1200) = 25 * 60 = 1500.

AI explanation

Using the simple interest formula, the interest for 14 months at 6 percent is (Principal * 6 * 14) / (12 * 100), which is 0.07 * Principal. The interest for 8 months at 8 percent is (Principal * 8 * 8) / (12 * 100), which is approximately 0.0533 * Principal. The difference is 0.07 * Principal - 0.0533 * Principal = 25. Solving 0.0167 * Principal = 25 gives a principal of Rs.1,500.

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