Multiple choice

If the compound interest for $2$ years on a certain sum be Rs. $84$ and the simple interest for $3$ years on the same sum be Rs. $120$, the sum will be-

  1. Rs. $565$
  2. Rs. $450$
  3. Rs. $515$
  4. Rs. $400$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

SI for 3 years = 120, so SI for 1 year = 40. For 2 years, SI = 80. CI for 2 years = 84. The difference (4) is the interest on the first year's interest. 4/40 = 10% rate. Principal = 40 / 0.10 = 400.

AI explanation

From the simple interest of Rs. 120 for 3 years, the annual interest is 120 / 3 = Rs. 40, meaning the SI for 2 years is Rs. 80. The difference between the given compound interest for 2 years (Rs. 84) and the simple interest for 2 years (Rs. 80) is Rs. 4, which is the interest earned on the first year's interest. Thus, the rate is (4 / 40) * 100 = 10%. Using the SI formula, the principal is (40 * 100) / 10 = Rs. 400.

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