Question : The marked price of 85 items was equal to the cost price of 153 items. The selling price of 104 items was equal to the marked price of 65 items. Calculate the percentage profit or loss from the sale of each item.
Option 1: 12.5% loss
Option 2: 12.5% profit
Option 3: 15% profit
Option 4: 12.25% profit
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Correct Answer: 12.5% profit
Solution :
Let the cost price of 1 item be Rs. 100.
So, the marked price of 85 items = Rs. 153 × 100 = Rs. 15300
⇒ The marked price of one item = Rs. $\frac{15300}{85}$ = Rs. 180
Also, the selling price of 104 items = marked price of 65 items
= Rs. 180 × 65
⇒ The selling price of 1 item = Rs. $\frac{180 × 65}{104}$
= Rs. 112.5
Profit % = $\frac{SP-CP}{CP}\times 100$
Where $SP$ is the selling price and $CP$ is the cost price.
So, profit % = $\frac{112.5 - 100}{100}\times 100$
= 12.5%
Hence, the correct answer is 12.5% profit.
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