Multiple choice

Passage

Each of the questions below consists of a question and two statements numbered (I) and (II) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and given answer.

What is the rate of simple interest per annum? (I) The sum triples in 20 years at simple interest. (II) The difference between the sum and the simple interest earned after 10 years is Rs. 1000.

  1. Statement (I) alone is sufficient, but statement (II) alone is not sufficient.

  2. Statement (II) alone is sufficient, but statement (I) alone is not sufficient.

  3. Both statements together are sufficient, but neither statement alone is sufficient.

  4. Each statement alone is sufficient.
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A Correct answer
Explanation

Statement I: Sum triples in 20 years, so SI = 2P. 2P = P * R * 20 / 100, so R = 10%. Statement II: P - SI = 1000. P - (P * R * 10 / 100) = 1000. P(1 - 0.1R) = 1000. This has two variables, so it's insufficient.

AI explanation

Statement I states that a sum triples in 20 years, meaning the simple interest earned equals twice the principal. Using the simple interest formula, 2P = P * R * 20 / 100, we solve to find R = 10%. Statement II only provides the difference between the principal and interest after 10 years, which yields P - (P * R * 10 / 100) = 1000, an equation with two variables that cannot be solved without knowing P or R. Statement I alone is sufficient to answer the question.

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