| 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 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,$$ Profit \ \% = \left[ \left( \frac{x - y}{y}\right) \times 100\right] $$ $$ 20 = \left[ \left( \frac{X - 12}{12}\right) \times 100\right] $$ $$ 2400 = (X - 12) \times 100 $$ $$ X = 14.4 \ Bananas $$