Multiple choice

If the simple interest on a certain sum of money for 3 years is Rs. 225 and the compound interest on the same sum at the same rate for 2 years is Rs. 153, then the principal invested (in Rs.) is

  1. Rs. 3000

  2. Rs. 1875

  3. Rs. 1500

  4. Rs. 2250

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

SI for 3 years = 225, so SI for 1 year = 75. Rate R = (75/P)*100. CI for 2 years = P(1+R/100)^2 - P = 153. P(1 + 75/P)^2 - P = 153. P(1 + 150/P + 5625/P^2) - P = 153. 150 + 5625/P = 153. 5625/P = 3. P = 1875.

AI explanation

Since the simple interest for 3 years is Rs. 225, the simple interest for 1 year is 225 divided by 3, which is Rs. 75, making the simple interest for 2 years Rs. 150. The compound interest for 2 years is Rs. 153, so the extra interest of 153 minus 150, which is Rs. 3, represents the interest on the first year's interest of Rs. 75. The rate is 3 divided by 75 multiplied by 100, which is 4 percent, and the principal is 75 divided by 4 multiplied by 100, equaling Rs. 1875. The result is Rs. 1875.

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