Question : The cost of a pencil is $33\frac{1}{3}$% less than the cost price of a pen. If a man sells 4 pencils at the cost price of 5 pens, what is his profit percentage?
Option 1: 50
Option 2: 66.66
Option 3: 75
Option 4: 87.5
Correct Answer: 87.5
Solution :
Let $x$ be the cost price of a pen.
Cost price of a pencil $= x - 33\frac{1}{3}$% of $x$ = $x - \frac{1}{3}x = \frac{2}{3}x$
Cost price of 4 pencils = $4 × \frac{2}{3}x$ = $\frac{8}{3}x$
Selling price of 4 pencils = cost price of 5 pens = $5x$
Profit percentage = $\frac{5x-\frac{8}{3}x}{\frac{8}{3}x}$×100 = $\frac{15x-8x}{8x}$×100 = 87.5%
Hence, the correct answer is 87.5.
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