Question : Sukhen purchased some perishable items for sale, but 15% of those items could not be sold and went bad. However, Sukhen managed to sell the rest of the items at a price that helped him earn an overall profit of 19%. At what percentage above the cost price of each item did Sukhen sell each of the items that did not go bad?
Option 1: 40%
Option 2: 42%
Option 3: 34%
Option 4: 36%
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Correct Answer: 40%
Solution : Let the cost of one item be Re. 1. $\therefore$ Cost of 100 items will be Rs. 100. As 15% of the items went bad, Remaining items = 100 – 15 = 85 Overall profit = 19% ⇒ Selling price $= \frac{\text{Cost price}\times \text{Profit}\%}{100}+\text{Cost price}$ ⇒ Selling price $= \frac{100\times19}{100}+100$ ⇒ Selling price $= 19 +100$ ⇒ Selling price $= 119$ Now, 85 items must be sold for Rs.119. Profit = Selling price – Cost price $= 119 - 85 = 34$ $\therefore$ Profit % $= \frac{34}{85}\times 100 = 40$% Hence, the correct answer is 40%.
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