Same Selling Price Trap
Spot the guaranteed loss in the classic “same selling price” question.
\text{Loss\%} = \dfrac{x^2}{100}
1How it works
When two articles are sold at the same price, one at a profit of x% and the other at a loss of x%, the overall result is always a loss of x²/100 percent — never break-even.
2How to apply (in seconds)
- Identify the common percentage x.
- Loss% = x² / 100.
3Worked examples
Example 1 Worked solution
Q. Two articles are sold at the same price, one at 20% profit and one at 20% loss. Net result?
- x = 20.
- Loss% = 20² / 100 = 400 / 100.
✓ 4% loss
4When to use it
- ✦Profit-and-loss MCQs with equal selling prices.
5Cautions & tips
- !The result is always a loss, whatever the order of the two sales.