Question : 40 percent of the selling price of a fan is equal to $\frac4{5}$ of the cost price of the fan. What is the profit percentage?
Option 1: 150 percent
Option 2: 125 percent
Option 3: 100 percent
Option 4: 120 percent
Correct Answer: 100 percent
Solution :
Let's the cost price of the fan as CP and the selling price as SP
⇒ 40% × SP = $\frac{4}{5}$×CP
⇒ 0.4 × SP = $\frac{4}{5}$ × CP
Now, let's solve for the selling price SP:
⇒ SP = $\frac{\frac{4}{5}×CP}{0.4}$ = $\frac{4}{5}$ × $\frac{1}{0.4}$ × CP = 2 × CP
⇒ Profit Percentage = $\frac{\text{Selling Price − Cost Price}}{\text{cost price}}$×100 = $\frac{2 × CP – CP}{CP}$×100 = $\frac{CP}{CP}$×100 = 100%
Hence, the correct answer is 100%.
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