Multiple choice

Mike buys 100 pair of shoes and set a price to gain a profit of 40%.He sells 40 pair of shoes at marked price and offers a discount of 10% on 20 pair of shoes.However 15 pair of shoes found damage and he was unable to these pairs.He sells the remaining pair of shoes by Z% increase in marked price to have overall profit or 20%.Then Z is nearest to :

  1. 11

  2. 15

  3. 18

  4. 20
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let CP = 100 per pair. Total CP = 10,000. Target profit 20% = 12,000. Marked Price (MP) = 140. 40 pairs sold at 140 = 5,600. 20 pairs at 10% discount (126) = 2,520. 15 pairs damaged (0). Remaining 25 pairs sold at (140 + Z% of 140). Total revenue = 5600 + 2520 + 25(140 + 1.4Z) = 12000. 8120 + 3500 + 35Z = 12000. 11620 + 35Z = 12000. 35Z = 380. Z = 10.85, nearest to 11.

AI explanation

Assuming the cost price of one pair of shoes is 100, the total cost for 100 pairs is 10000, and the marked price for a 40% profit is 140 per pair. For an overall profit of 20%, the required total revenue is 120% of 10000, which is 12000. The revenue from the first 40 pairs is 40 x 140 = 5600, the revenue from the next 20 pairs at a 10% discount is 20 x 126 = 2520, and the 15 damaged pairs yield 0, leaving a remaining target of 12000 - 5600 - 2520 = 3880. There are 25 pairs left to sell, so the new selling price is 3880 / 25 = 155.2, which is an increase of 15.2 over the marked price of 140; calculating the percentage increase gives (15.2 / 140) x 100 = 10.85%, making 11 the nearest value.

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