Multiple choice

A sum of money becomes 6 times at 6.25% rate of simple interest. Find the rate at which it becomes 11 times.

  1. 13.5%

  2. 12.5%

  3. 12%

  4. 13%

  5. 14.5%
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B Correct answer
Explanation

Sum becomes 6 times, so SI = 5P. 5P = P * R * T / 100 => 5 = 6.25 * T / 100 => T = 500 / 6.25 = 80 years. To become 11 times, SI = 10P. 10P = P * R' * 80 / 100 => 10 = R' * 0.8 => R' = 10 / 0.8 = 12.5%.

AI explanation

Using the simple interest formula, if a sum becomes 6 times, the interest is 5 times the principal, so 5P equals (P times 6.25 times T) divided by 100, yielding a time period of 80 years. For the sum to become 11 times, the interest must be 10 times the principal, so we set 10P equals (P times R times 80) divided by 100. Solving for R gives 800 equals 10R, which results in a rate of 12.5%. The required rate is 12.5%.

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