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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