Question:medium

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 :

Updated On: Jan 13, 2026
  • statement (1) alone is sufficient to answer the question
  • statement (2) alone is sufficient to answer the question
  • both the statements together are needed to answer the question
  • either statement (1) alone or statement (2) alone is sufficient to answer the question
  • neither statement (1) nor statement (2) suffices to answer the question
Show Solution

The Correct Option is D

Solution and Explanation

The correct answer is option (D):
either statement (1) alone or statement (2) alone is sufficient to answer the question

Here's the breakdown of why the answer is "either statement (1) alone or statement (2) alone is sufficient to answer the question":

The core problem requires us to determine the percentage of the total amount spent on article A to fulfill the requirement. The key here is to figure out the effective number of article A's the person needs to *pay* for, considering the "buy 4 B, get 1 A free" offer.

Let's break down the problem and the sufficiency of each statement.

* Articles Needed: 1000 A, 800 B.
* Offer: For every 4 B purchased, 1 A is free.

To figure out how many free A's the person gets:

* The person needs to buy 800 B.
* For every 4 B bought, they get 1 free A.
* Number of free A's = 800 B / 4 = 200 free A's.

Therefore, the person effectively needs to *pay* for 1000 A - 200 A = 800 A.

Now, we need the relative price of A and B to calculate the amount spent on each. The percentage spent on A will be: (Cost of 800 A) / (Cost of 800 A + Cost of 800 B) * 100%

Let's analyze the statements:

* Statement 1: Ratio of price of article A to article B is 3 : 5

If we let the price of A be 3x and the price of B be 5x, we can calculate the total cost.
Cost of 800 A = 800 * 3x = 2400x
Cost of 800 B = 800 * 5x = 4000x
Total Cost = 2400x + 4000x = 6400x
% spent on A = (2400x / 6400x) * 100% = 37.5%
Statement 1 gives us enough information.

* Statement 2: Price of article A is one fourth of the price of article B

This means Price of A = (1/4) * Price of B
If the price of B is 4y, then the price of A is y.

Cost of 800 A = 800 * y = 800y
Cost of 800 B = 800 * 4y = 3200y
Total Cost = 800y + 3200y = 4000y
% spent on A = (800y / 4000y) * 100% = 20%
Statement 2 also gives enough information.

* Conclusion:

Both Statement 1 and Statement 2, when considered individually, provides enough information to calculate the percentage of amount spent on article A. We can use either the ratio or the direct price relationship to solve the problem. Therefore, the answer is "either statement (1) alone or statement (2) alone is sufficient to answer the question".
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Top Questions on Statements and Inferences

Questions Asked in IBSAT exam

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The result is not just a lofty declaration of principles but a blueprint for a practical programme of action. The policy delineates a series of concrete measures to accord women a decision-making role in the political domain and greater control over their economic status. Of especially far-reaching impact are the devolution of control of economic infrastructure to women, notably at the gram panchayat level, and the amendments proposed in the Hindu Succession Act of 1956 to give women coparcenary rights.
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