A man purchased two varieties of pens at the rates of ₹8 for 9 pens and ₹8 per pen. If he purchased an equal number of pens of each of the two varieties and then sold all his pens at ₹6 per pen, what was his profit percentage?
35%
Let's assume the man purchased \(x\) pens of each variety.
Cost of the first variety of pens:
The cost of 9 pens is ₹8. Therefore, the cost of 1 pen is \(\frac{8}{9}\) ₹. The cost of \(x\) pens is \(\frac{8x}{9}\) ₹.
Cost of the second variety of pens:
The cost of 1 pen is ₹8. The cost of \(x\) pens is \(8x\) ₹.
Total cost of pens:
Total cost = Cost of first variety + Cost of second variety = \(\frac{8x}{9} + 8x = \frac{8x + 72x}{9} = \frac{80x}{9}\) ₹
Total selling price of pens:
He purchased \(2x\) pens in total and sold them at ₹6 per pen. Total selling price = \(2x \times 6 = 12x\) ₹
Profit:
Profit = Selling price - Cost price = \(12x - \frac{80x}{9} = \frac{108x - 80x}{9} = \frac{28x}{9}\) ₹
Profit percentage:
Profit percentage = \(\frac{\text{Profit}}{\text{Cost price}} \times 100 = \frac{\frac{28x}{9}}{\frac{80x}{9}} \times 100 = \frac{28x}{80x} \times 100 = \frac{28}{80} \times 100 = \frac{7}{20} \times 100 = 35\%\)
Therefore, his profit percentage is 35%.
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