Multiple choice

Passage

Directions: The following problem consists of a question followed by three statements (I), (II), and (III). You have to determine which statement(s) is/are sufficient /necessary to answer the question.

Find the cost price of the article. I. The difference between the marked price and the cost price of the article is Rs. 125. II. A profit of 10% was made by selling that article after giving a discount of 12%. III. The difference between the selling price and the marked price is Rs. 75.

  1. Only I and II

  2. Only I and III

  3. Only II and either I or III

  4. Any two statements

  5. All three statements
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP = x, MP = y. I: y - x = 125. II: SP = 0.88y, Profit = 10%, so SP = 1.1x. Thus 0.88y = 1.1x, or y = 1.25x. III: SP - y = 75 (this implies SP > MP, which is impossible for a discount, likely meant y - SP = 75). Using II (y = 1.25x) and I (y - x = 125), we get 1.25x - x = 125, 0.25x = 125, x = 500. Statement III is redundant if I and II are used.

AI explanation

Using the successive percentage formula, the overall profit percentage is calculated as 10 minus 12 plus (10 times -12 divided by 100), which equals -3.2%, meaning the selling price is 96.8% of the marked price. Let the marked price be M, cost price be C, and selling price be S. Statement II relates the three variables with the equation 0.968M = S, while statement I provides the equation M - C = 125, and statement III provides the equation M - S = 75. To find C, statement II is strictly necessary to define the relationship between M and S in terms of C, and then either statement I or III can be used to substitute and solve for the values.

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