Question : A dishonest dealer defrauds to the extent of $x$% in buying as well as selling his goods by using a faulty weight. What will be the gain percentage on his outlay?
Option 1: $2x$%
Option 2: $\left (\frac{10}{x} +x^{2}\right )$%
Option 3: None of these
Option 4: $\left (x+\frac{x^{2}}{100} \right)$%
Correct Answer: None of these
Solution :
Given: A dishonest dealer defrauds to the extent of $x$% in buying as well as selling.
Let the total cost of an article be Rs. 100.
The cost price (CP) of that article for the dishonest dealer = Rs. (100 – $x$)
The selling price (SP) of that article for the dishonest dealer = Rs. (100 + $x$)
Profit = SP – CP = (100 + $x$) – (100 – $x$) = Rs. $2x$
Therefore, the profit percentage = $\frac{\text{Profit}}{\text{CP}}×100$ = ($\frac{2x}{100-x}×100$)%
This is not among the options.
Hence, the correct answer is "None of these".
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