Multiple choice

Directions: The question given below is followed by two statements A and B. You have to determine which statements(s) is/are sufficient/necessary to answer the question. What is the sum of money? A. The difference between compound interest and simple interest on a certain sum of money for 2 years at 7% is Rs. 44.1. B. The compound interest for 2 years at 20% is Rs. 1800.

  1. Statement A alone is sufficient to answer the question, but statement B alone is not sufficient to answer the question.

  2. Statement B alone is sufficient to answer the question, but statement A alone is not sufficient to answer the question.

  3. Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.

  4. Either statement A or statement B by itself is sufficient to answer the question.

  5. Statements A and B taken together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement A: Difference between CI and SI for 2 years = P * (r/100)^2. With r=7, 44.1 = P * (0.07)^2, so P can be found. Statement B: CI = P * ((1 + r/100)^n - 1). With r=20, 1800 = P * ((1.2)^2 - 1), so P can be found. Both are sufficient independently.

AI explanation

From statement A, using the formula for the difference between compound interest and simple interest for 2 years, Difference = Principal * (Rate/100)^2, we substitute the values to get 44.1 = Principal * (7/100)^2. This gives Principal * 0.0049 = 44.1, which allows us to solve and find the principal is Rs. 9000. From statement B, the compound interest for 2 years at 20% means the amount becomes 1.44 times the principal, so 0.44 * Principal = 1800, which also allows us to find the principal sum of Rs. 4090.91. Therefore, either statement A or statement B by itself is sufficient to answer the question.

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