# If Selling Price is Equal to Cost Price then Profit and Loss in Aptitude:

#### Overview:

 Topic Included: Formulas, Definitions & Exmaples. Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Profit and Loss Aptitude Notes & Questions. Questions for practice: 10 Questions & Answers with Solutions.

#### If Selling Price is Equal to Cost Price then Profit and Loss:

If the cost price of $$x$$ item is equal to the selling price of $$y$$ item, then- $$Profit \ \% \ or \ Loss \ \% = \left( \frac{x - y}{y}\right) \times 100$$

Note: If the value of $$x$$ is greater than $$y$$, $$(x \gt y)$$ then there will be profit, and if the value of $$x$$ is less than $$y$$, $$(x \lt y)$$ then there will be loss.

Example (1): If the cost price of $$10$$ mangoes is equal to the selling price of $$8$$ mangoes then, find the profit or loss percent $$(\%)$$ of the seller?

Solution:Given values, $$x = 10$$, $$y = 8$$, Here $$(x \gt y)$$ so there will be profit, then according to formula given above,$$Profit \ \% = \left[ \left( \frac{x - y}{y}\right) \times 100\right]$$ $$Profit \ \% = \left[ \left( \frac{10 - 8}{8}\right) \times 100\right]$$ $$Profit \ \% = \frac{2}{8} \times 100$$ $$Profit \ \% = \frac{200}{8} = 25 \ \%$$

Example (2): If the cost price of $$1 \ kg$$ of Sugar is equal to the selling price of $$1.5 \ kg$$ Sugar, then find the profit or loss percent $$(\%)$$ of the seller?

Solution:Given values, $$x = 1 \ kg$$, $$y = 1.5 \ kg$$, Here $$(x \lt y)$$ so there will be loss, then according to formula given above,$$Loss \ \% = \left[ \left( \frac{x - y}{y}\right) \times 100\right]$$ $$Loss \ \% = \left[ \left( \frac{1 - 1.5}{1.5}\right) \times 100\right]$$ $$Loss \ \% = \frac{- 0.5}{1.5} \times 100$$ $$Loss \ \% = \frac{- 50}{1.5} = - 33.33 \ \%$$ Here $$(-)$$ sign indicates the loss.

Example (3): The selling price of $$12$$ Bananas is equal to the cost price of $$X$$ Bananas, If the seller made a profit of $$20 \ \%$$ find the value of $$X$$?

Solution:Given values, $$x = X$$, $$y = 12$$, and there is a profit as given in the question, then according to formula given above,$$Profit \ \% = \left[ \left( \frac{x - y}{y}\right) \times 100\right]$$ $$20 = \left[ \left( \frac{X - 12}{12}\right) \times 100\right]$$ $$2400 = (X - 12) \times 100$$ $$X = 14.4 \ Bananas$$