Multiple choice

Directions: The following problem consists of a question and two statements numbers I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. Read the both the statements and mark your answer accordingly. A borrowed some amount of money at simple interest. At the end of 9 years, he paid a total interest Rs. 22,800. What was the amount of money he borrowed in the beginning? Statement I: A borrowed the money at the rate of 6% per annum for initial two years and then his rate of interest increased by 3% for the next three years. Statement II: A borrowed the money at the rate of 14% for the remaining time period after 5 years.

  1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. The data in both statements I and II together is necessary to answer the question.

  4. The data in statement I alone or in statement II alone is sufficient to answer the question.

  5. The data in both statements I and II is not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the principal, we need the total interest and the rates over time. Statement I gives rates for the first 5 years. Statement II gives the rate for the remaining 4 years. Combining both allows us to calculate the weighted average interest rate over 9 years, which is necessary to solve for the principal.

AI explanation

Using the formula for simple interest, SI = PRT / 100, we know the total interest for 9 years is 22800. Let the principal be P; from the two statements combined, the interest rate is 6% for the first 2 years, 9% for the next 3 years, and 14% for the remaining 4 years. This gives the equation P(6*2 + 9*3 + 14*4) / 100 = 22800, which simplifies to 95P / 100 = 22800. Because neither statement provides the complete interest rate breakdown for all 9 years individually, both statements together are necessary to solve for the principal.

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