Multiple choice

Directions: The question given below is followed by two statements A and B. You have to determine which statement(s) is/are sufficient/necessary to answer the question. What is the rate of interest per annum? (A) The amount invested by a person is Rs. 10,000 and the difference between Compound interest and Simple Interest is Rs. 144 in two years. (B) The amount invest by the person is Rs. 10,000 and becomes Rs. 14,049.28 in three years at compound interest.

  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 allows calculating the rate using the formula for CI-SI difference for 2 years. Statement B allows calculating the rate using the compound interest formula for 3 years. Both are independently sufficient.

AI explanation

From statement A, the formula for the difference between compound interest and simple interest for two years is Principal multiplied by rate squared divided by 10000. Substituting the given values gives 10000 multiplied by rate squared divided by 10000 equals 144, which means the rate squared equals 144, so the rate is 12%. From statement B, using the compound interest formula we solve 14049.28 equals 10000 multiplied by the quantity (1 plus rate divided by 100) cubed. This yields 1 plus rate divided by 100 equals 1.12, confirming the rate is 12%. Both statements independently provide a unique rate.

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