Multiple choice

Passage

Directions: Study the table carefully and answer the given question. The following table shows details of profit and loss percentages after providing discounts on 4 different items I, II, III and IV. Seller Item I Item II Item III Item IV A Profit % = 20 Loss % = 5 - - B Loss % = 10 - Profit % = 22 - C - - Profit % = 18 Loss % = 3 D Profit % = 15 Profit % = 15 - Profit % = 13 E - Loss % = 2 Loss % = 12 Profit % = 23

If the average selling price of item III for sellers B, C and E is Rs. 4820 and marked price of item III is twice the cost price of item III for seller B, 3/2 times the cost price of the same for seller C, and 4/3 times the cost price of the same for seller E, and also, marked price of item III for all the three sellers is the same, then what is the discount percentage provided by seller E?

  1. 6%

  2. 12%

  3. 24%

  4. 34%

  5. No discount is provided.
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D Correct answer
Explanation

The average selling price for item III is 4820. Let MP be the marked price. For B, C, and E, the cost prices are MP/2, 2MP/3, and 3MP/4 respectively. Selling prices are SP_B = MP(1-d_B), SP_C = MP(1-d_C), SP_E = MP(1-d_E). Using profit percentages (Profit = (SP-CP)/CP), we find the discounts. This requires solving the system of equations based on the profit percentages provided in the table.

AI explanation

Let the marked price be M. Using the selling price formula, selling price equals marked price times (1 minus discount percentage). The cost prices for sellers B, C, and E are M/2, 2M/3, and 3M/4, respectively. The selling prices are calculated as 1.22 times M/2, 1.18 times 2M/3, and 0.88 times 3M/4, resulting in 0.61M, 0.7867M, and 0.66M. The average selling price is 4820, so the sum of the selling prices is 14460, which gives 2.0567M equals 14460, meaning M is approximately 7030. The selling price for seller E is 0.66 times 7030, which is approximately 4640, and the discount amount is 7030 minus 4640 equals 2390; dividing 2390 by 7030 gives a discount of approximately 34%.

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