Multiple choice

Sherlock invested some money in a scheme that follows the rule of simple interest. What was the time period for which he invested his money, if the rate of interest was 10%? 1. The interest he received was 1 10 of the principal. 2. He received $1,000 as interest.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
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A Correct answer
Explanation

Statement 1: Interest = 1/10 of Principal. Since Interest = (P*R*T)/100, 0.1P = (P*10*T)/100. 0.1 = 0.1T, so T = 1 year. This is sufficient. Statement 2: Interest = 1000. We don't know the principal, so we cannot find T. Thus, only (1) is sufficient.

AI explanation

Using the simple interest formula, T = (100 * SI) / (P * R). Statement 1 gives the interest as 1/10 of the principal, meaning SI = 0.10P. Substituting this into the formula yields T = (100 * 0.10P) / (P * 10) = 1 year, so statement 1 alone is sufficient to find the time period. Statement 2 only provides the interest as $1,000 without giving the principal, so it cannot determine the time alone. Therefore, only statement 1 is sufficient.

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