Question

A person wants to purchase 1,000 pieces of article A and 800 pieces of article B. There is an offer price on these two articles that for every purchase of 4 pieces of article B, 1 piece of article A is given free. What percentage of amount should he spend on article A to fulfill his requirement?
Statement 1: Ratio of price of article A to article B is 3 : 5
Statement 2: Price of article A is one fourth of the price of article B
Directions: This question has a problem and two statements numbered (1) and (2) giving certain information. You have to decide if the information given in the statements is sufficient for answering the problem. Indicate your answer :

• A. statement (1) alone is sufficient to answer the question
• B. statement (2) alone is sufficient to answer the question
• C. both the statements together are needed to answer the question
• D. either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is D

To solve this problem, we need to determine the percentage of the amount spent on article A given certain conditions. We'll analyze each statement separately to see if it is sufficient to answer the question.

1. Understanding the Offer:
   • For every 4 pieces of article B purchased, 1 piece of article A is given free. For 800 pieces of article B, the person gets 200 pieces of article A for free.
   • The person requires 1,000 pieces of article A. Therefore, they need to purchase \(1,000 - 200 = 800\) pieces of article A.
2. Statement 1: The ratio of the price of article A to article B is 3:5.
   • Let the price of article A be \(3x\) and article B be \(5x\).
   • The cost for purchasing 800 pieces of article A = \(800 \times 3x = 2,400x\).
   • The cost for purchasing 800 pieces of article B = \(800 \times 5x = 4,000x\).

   This information allows us to calculate the percentage of amount spent on article A:

   \[\frac{{2,400x}}{{2,400x + 4,000x}} \times 100\ = \frac{{2,400x}}{{6,400x}} \times 100 = 37.5\%\]

   This calculation shows that statement 1 alone is sufficient.

3. Statement 2: The price of article A is one fourth of the price of article B.
   • Let the price of article B be \(4x\). Then, the price of article A is \(x\).
   • The cost for purchasing 800 pieces of article A = \(800 \times x = 800x\).
   • The cost for purchasing 800 pieces of article B = \(800 \times 4x = 3,200x\).

   With this statement, we can also calculate the percentage of amount spent on article A:

   \[\frac{{800x}}{{800x + 3,200x}} \times 100\ = \frac{{800x}}{{4,000x}} \times 100 = 20\%\]

   This shows that statement 2 alone is sufficient.

Conclusion: Either statement (1) alone or statement (2) alone is sufficient to answer the question.