Question : There is a profit of 10% when an item is sold at $\frac{5}{6}$ of its actual selling price. What will be the profit percentage on the cost price when the item is sold at its actual selling price?
Option 1: 28%
Option 2: 32%
Option 3: 26%
Option 4: 30%
Correct Answer: 32%
Solution :
When the item is sold at $\frac{5}{6}$ of its actual selling price, there is a profit of 10%
Profit = $\frac{5}{6}S−C$ = 0.10$C$ where $S$ is actual selling price and $C$ is cost price.
⇒ $5S − 6C = 0.60C$
⇒ $5S = 6.60C$
⇒ $S = \frac{6.60C}{5}$
⇒ $S = 1.32C$
⇒ Profit = $\frac{1.32C - C}{C} × 100$%
⇒ Profit % = 32%
Hence, the correct answer is 32%.
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