Multiple choice

Simple interest on a certain amount is $\displaystyle\frac{9}{16}$ of the principal. If the number representing the rate of interest in percent and time in years be equal, then the time for which the principal amount is lent out is

  1. $\;5\displaystyle\frac{1}{2}$ years
  2. $\;6\displaystyle\frac{1}{2}$ years
  3. $\;7$ years
  4. $\;7\displaystyle\frac{1}{2}$ years
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D Correct answer
Explanation

SI = (P * R * T) / 100. Given SI = (9/16)P and R = T. (9/16)P = (P * R * R) / 100. R^2 = 900 / 16. R = 30 / 4 = 7.5. Since R = T, time = 7.5 years.

AI explanation

Let the principal be P. The simple interest is (9/16)P. Using the simple interest formula, Simple Interest = (Principal x Rate x Time) / 100, we get (9/16)P = (P x R x T) / 100. Since the rate and time are equal, let R = T = x, so (9/16)P = (P x x^2) / 100. Solving for x^2 yields 900/16, which means x = 30/4 = 7.5. The time is 7 and a half years.

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