Question

What was the cost price of the suitcase purchased by Samir? I. Samir got a 25 percent concession on the labelled price. II. Samir sold the suitcase for Rs. 2000 with 25 percent profit on the labelled price.

• A. if 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.
• B. if 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.
• C. if the data in both the statements I and II together are not sufficient to answer the question.
• D. if the data in both the statements I and II together are necessary to answer the question.

Hint:

When solving such problems, check if you need both statements to arrive at the correct answer. In this case, both were necessary.

Answer 1

The Correct Option is D

Step 1: From statement I, we know that Samir got a 25% concession on the labelled price. Let the labelled price be \( L \), so Samir paid \( 0.75L \) for the suitcase. 
Step 2: From statement II, we know that Samir sold the suitcase for Rs. 2000 with a 25% profit on the labelled price. The selling price is \( 1.25L \), so: \[ 1.25L = 2000. \] Solving for \( L \): \[ L = \frac{2000}{1.25} = 1600. \] 
Step 3: Now, using statement I, the cost price is: \[ 0.75L = 0.75 \times 1600 = 1200. \] Thus, the cost price of the suitcase is Rs. 1200, which requires both statements.