Multiple choice

The difference between compound interest and simple interest for $3$ years @ $20\% p.a.$ is $152$. What is the principal lent?

  1. $Rs. 1200$
  2. $Rs. 1155$
  3. $Rs. 1187.50$

  4. None of these
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C Correct answer
Explanation

Difference for 3 years = P * (r/100)^2 * (3 + r/100). 152 = P * (0.2)^2 * (3.2) = P * 0.04 * 3.2 = P * 0.128. P = 152 / 0.128 = 1187.50.

AI explanation

Using the formula for the difference between compound interest and simple interest for three years, we have Difference = P(R/100)^2(3 + R/100). Substituting the given values 152 = P(20/100)^2(3 + 20/100), which simplifies to 152 = P(0.04)(3.2). Solving for the principal gives P = 152 / 0.128, resulting in a principal of Rs. 1187.50.

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