Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. The ratio of the cost price of article A to that of article B is 5 : 3. What is the profit percentage on article B? 1. The ratio of the selling price of article A to that of article B is 4 : 7. 2. The difference between the cost prices of articles A and B is Rs. 200 and the difference between the selling prices of articles B and A is Rs. 300.

  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 (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Both statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP_A = 5x, CP_B = 3x. Statement 1 gives SP_A/SP_B = 4/7. We cannot find the profit percentage without knowing the absolute values. Statement 2 gives CP_A - CP_B = 2x = 200, so x = 100. CP_A = 500, CP_B = 300. SP_B - SP_A = 300. We have two variables (SP_A, SP_B) and one equation. Combining both, we have ratios and differences, which is sufficient.

AI explanation

The cost price ratio is 5 to 3, meaning if the cost prices are 5x and 3x, we need the selling price of article B to find its profit percentage. Statement 1 gives the selling price ratio but provides no absolute values to link it to the cost price ratio. Statement 2 provides the absolute difference in cost prices, allowing us to find x equals 100 rupees, making the cost prices 500 rupees and 300 rupees, but it only gives the difference in selling prices without their individual values. Using both statements together, the selling prices are in a 4 to 7 ratio with a difference of 300 rupees, meaning the selling price of article B is 7 parts, which equals 700 rupees, and its profit is 700 minus 300, which is 400 rupees on a cost of 300 rupees, allowing us to calculate the profit percentage. Both statements together are sufficient, but neither alone is sufficient.

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