The selling prices of two articles are equal. If the first article is sold at a profit of 20% and the second article is sold at a loss of 20%, what will be the overall loss percentage?

Let's assume the cost price of the first and second articles are '10y' and '10z' respectively.

If the first article is sold at a profit of 20% and the second article is sold at a loss of 20%.

selling price of the first article = 10y of (100+20)%

= 10y of 120%

= 12y

selling price of the second article = 10z of (100-20)%

= 10z of 80%

= 8z

The selling prices of two articles are equal.

12y = 8z

3y = 2z

$$\frac{y}{z}\ =\ \frac{2}{3}$$

Let's assume y = 2a and z = 3a.

Total cost price = 10y+10z

= $$10\times2a+10\times3a$$

= 20a+30a

= 50a

Total selling price = 12y+8z

= $$12\times2a+8\times3a$$

= 24a+24a

= 48a

Overall loss percentage = $$\frac{\left(total\ cost\ price-total\ selling\ price\right)}{total\ cost\ price}\times100$$

= $$\frac{\left(50a-48a\right)}{50a}\times100$$

= $$\frac{2a}{50a}\times100$$

= $$\frac{1}{25}\times100$$

= 4%