Multiple choice

If the compound interest on a certain sum for three years at $10\%$ is Rs. $993$, What would be the simple interest on the same sum at the same rate for the same time ?

  1. Rs. $930$
  2. Rs. $920$
  3. Rs. $900$
  4. Rs. $890$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

CI = P * ((1 + r/100)^n - 1). 993 = P * ((1.1)^3 - 1) = P * (1.331 - 1) = 0.331P. P = 993 / 0.331 = 3000. SI = P * r * t / 100 = 3000 * 0.1 * 3 = 900.

AI explanation

For a principal P, the difference between the compound interest and simple interest over 3 years at 10% is given by the formula P * (R / 100)^2 * (3 + R / 100). Substituting the known values gives the difference as P * (0.1)^2 * 3.1 = 0.031P. Since the difference between the given compound interest of Rs. 993 and the unknown simple interest is 0.031P, and the simple interest itself is 0.3P, we can write the ratio 0.3P / 0.031P = SI / (993 - SI). Solving this proportion gives 0.3 * (993 - SI) = 0.031 * SI, which simplifies to 297.9 = 0.331 * SI, resulting in a simple interest of Rs. 900.

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