A retailer buys 20 pens at the marked price of 15 pens from a wholesaler. If he sells these 20 pens giving a discount of 1%, then what is the profit percent of the retailer?

The retailer buys 20 pens at the marked price of 15 pens.

He gives a discount of 1% when selling the pens.

The retailer is essentially getting 20 pens at the cost of 15 pens, which means he is buying each pen at a lower price.

Cost Price (C.P.) per pen:

​$$C.P. = \frac{\text{Marked Price of 15 pens}}{20} \text{ (since he buys 20 pens at the cost of 15 pens)}$$​​

Selling Price (S.P.) per pen:

​$$S.P. = \text{Marked Price of 1 pen} - \text{1\% discount on Marked Price}$$​​

Profit Percent:

​$$\text{Profit Percent} = \frac{\text{S.P.} - \text{C.P.}}{\text{C.P.}} \times 100$$​​

Solution:

Let the marked price of each pen be x.

Cost Price for each pen: Since the retailer buys 20 pens at the price of 15 pens, the cost price per pen is:

​$$C.P. = \frac{15x}{20} = \frac{3x}{4}$$​​

Selling Price for each pen: The retailer gives a discount of 1%, so the selling price per pen is:

​$$S.P. = x - \frac{1}{100} \times x = x - 0.01x = 0.99x$$​​

Profit Percent:

​$$\text{Profit Percent} = \frac{0.99x - \frac{3x}{4}}{\frac{3x}{4}} \times 100 \\ \ \\\text{Profit Percent} = \frac{0.99x - 0.75x}{0.75x} \times 100 = \frac{0.24x}{0.75x} \times 100 = 32\%$$​​

Thus, the profit percentage of retailer = 32%