Question

A shopkeeper by selling 21 Nike shoes, earns a profit equal to the selling price of 5 Nike shoes. His profit percentage is

A) 31.25 percent B) 23.8 percent C) 47.6 percent D) 16.35 percent

Answer 1

Given :

Shopkeeper is selling 21 Nike shoes.

Profit made by the shopkeeper is equal to the selling price of 5 Nike shoes.

To find :

Profit percentage of the shopkeeper

Solution:

Let the cost price of one Nike shoe = $C

Cost of 21 Nike shoes = $21C

And the selling price of one Nike shoe = $S

Selling price of 21 Nike shoes = $21S

Profit earned by the shopkeeper = Selling price - Cost price

= $21S - $21C

Selling price of 5 Nike shoes = $5S

Profit earned is equal to the selling price of 5 Nike shoes.

21S - 21C = 5S

21S - 5S = 21C

16S = 21C

$\frac{C}{S}=\frac{16}{21}$

Since profit percentage = $\frac{\text{Profit}}{\text{Cost price}}\times 100$

                                        = $\frac{(S-C)}{S}\times 100$

                                        = $(1-\frac{C}{S})\times 100$

                                        = $(1-\frac{16}{21})\times 100$

                                        = $\frac{5\times 100}{21}$

                                        = 23.8%

Therefore, his profit percentage is 23.8%

Option (B) will be the answer.