A seller sold two shoes at the same selling price.

[Gmat_mission]

A seller sold two shoes at the same selling price. If the percentage profit on one of the shoes was 30% and the percentage loss on the other shoe was 30%, find the overall percentage profit or loss made by the seller.

A. 3% loss
B. 3% profit
C. 9% loss
D. 9% profit
E. No profit no Loss

[spoiler]OA=C[/spoiler]

Source: e-GMAT

[Vincen]

A seller sold two shoes at the same selling price. If the percentage profit on one of the shoes was 30% and the percentage loss on the other shoe was 30%, find the overall percentage profit or loss made by the seller.

A. 3% loss
B. 3% profit
C. 9% loss
D. 9% profit
E. No profit no Loss

[spoiler]OA=C[/spoiler]

Source: e-GMAT

Hi Gmat_mission.

Let's suppose he sold each pair of shoes for 100.

For the pair of shoes Nº 1 he got a profit of 30%, therefore, let's calculate the cost price of the shoe: $$Cost_{price}=x+30\%\cdot x=1.3x=100\ \ \Rightarrow\ \ x=76.92.$$ For the pair of shoes Nº2 he lost 30%. So the cost price was $$Cost_{price}=x-30\%\cdot x=0.7x=100\ \ \Rightarrow\ \ x=142.85.$$ Hence, the total cost price for both pair of shoes was 76.92+142.85=219.77, but the seller sold them for 100+100=200.

So, the seller had a lost of 219.77-200=19.77.

Let's see what percentage it represents. $$p=\frac{19.77}{219.77}\cdot100=8.99\%.$$ In conclusion, the overall percentage loss made by the seller was 9%.

So, the correct answer is the option _C_.

I hope it helps you. <i class="em em-sunglasses"></i>

[Scott@TargetTestPrep]

A seller sold two shoes at the same selling price. If the percentage profit on one of the shoes was 30% and the percentage loss on the other shoe was 30%, find the overall percentage profit or loss made by the seller.

A. 3% loss
B. 3% profit
C. 9% loss
D. 9% profit
E. No profit no Loss

[spoiler]OA=C[/spoiler]

Source: e-GMAT

We can let the selling price of each shoe = $91. Thus, for the shoe that has a 30% profit, the cost, x, can be determined by the equation:

x(1.3) = 91

x = 91/1.3 = 70

Likewise, for the shoe that has a 30% loss, the cost, y, can be determined by the equation:

y(0.7) = 91

x = 91/0.7 = 130

Therefore, the total cost of the two shoes is 70 + 130 = $200, and the total revenue from selling the two shoes is 2(91) = $182. Therefore, the percent change is (182 - 200)/200 = -18/200 = -9%, i.e., the seller has a 9% loss.

Answer: C