Question

The selling price of two articles is the same. If one article is sold at 20% loss and another at 20% profit, then find the profit or loss percentage on the whole transaction.

• A. No profit no loss
• B. 4% loss
• C. 4% profit
• D. 44% profit

Answer 1

The correct option is B 4% loss

Let the selling price of each article be 120.
Now, we have 20% profit at first; so,
⇒ 120% of CP₁ = 120
⇒ CP₁ = 120 × (100/120) = 100
Also, we have 20% loss; so,
⇒ 80% of CP₁ = 120
⇒ CP₁ = 120 × (100/80) = 150
Hence,
Total SP = 120 + 120 = 240
Total CP = 100 + 150 = 250
Loss = 250 – 240 = 10
Loss% = (10/250) × 100 = 4%

Short Cut-
If the selling price is the same and we have the same percentage of profit and loss,
there will always be a loss of $\left(\frac{x^2}{100}\right)$%=$\frac{{20}^2}{100}$%=4% loss.