Question : Sukhvir purchased some perishable items for sale but 30% of those items could not be sold and went bad. However, Sukhvir 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 purchased by Sukhvir did he sell each of the items that did not go bad?
Option 1: 49%
Option 2: 70%
Option 3: 63%
Option 4: 75%
Correct Answer: 70%
Solution :
Let C as the cost price of each item, S as the selling price of each item that did not go bad and n as the total number of items.
From the problem, 30% of the items went bad, so Sukhvir sold 70% of the items. The overall profit was 19%.
The total cost price = nC
The total selling price = nC + 0.19nC = 1.19nC
The total selling price = 0.7nS (because Sukhvir sold 70% of the items)
⇒ 1.19nC = 0.7nS
⇒ S = $\frac{1.19C}{0.7}$ = 1.7C
$ \text{Profit percentage}=\frac{\text{Profit}}{\text{Cost price}}\times 100$
$=\frac{\text{0.7C}}{\text{C}}\times 100$
= 70%
Hence, the correct answer is 70%.
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