Multiple choice

Directions: The following question is accompanied by statements A and B. You have to determine which statement(s) is/are sufficient/necessary to answer the question. Find the amount received by Mr. Goyal at the end of 2 years, if the rate of interest is 12% compounded annually. (A) Mr. Goyal invested the same amount of money under simple interest at the rate of 15% per annum and received a total amount of Rs. 24,000 at the end of 4 years. (B) The difference between compound interest and simple interest on the same sum of money at 10% of interest at the end of 2 years is Rs. 150.

  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 us to find the principal (P) using SI = P*R*T/100, which is sufficient to calculate the compound interest amount. Statement B provides the difference between CI and SI for 2 years, which is P*(R/100)^2, allowing us to find P and subsequently the compound interest amount. Since both statements independently provide the necessary information to find the principal, either is sufficient.

AI explanation

From statement A, using the simple interest amount formula Amount = Principal * (1 + Rate * Time / 100), we substitute the values to get 24000 = Principal * (1 + 15 * 4 / 100), which simplifies to 24000 = 1.6 * Principal, allowing us to find the principal sum of Rs. 15,000. From statement B, applying the 2-year difference formula Difference = Principal * (Rate/100)^2 gives 150 = Principal * (10/100)^2, which means Principal * 0.01 = 150, also allowing us to find the principal sum of Rs. 15,000. Since both statements independently allow us to find the principal, we can then use the compound interest formula Amount = Principal * (1 + Rate/100)^Time to find the final amount. Therefore, either statement A or statement B by itself is sufficient to answer the question.

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