Practice Profit and Loss Questions and Answers 2024

Rule	Description
1	If S.P. > C.P. then there will be profit. Profit = S.P. – C.P. Profit % = \[\frac{Profit \times 100}{C.P.}\] Note: Both profit and loss are always calculated on cost price only.
2	If C.P. > S.P. then there will be profit. Loss = C.P. - S.P. Loss % = \[\frac{Loss \times 100}{C.P.}\]
3	If an object is sold on r% Profit, then S.P. = \[C.P.\left[\frac{100 + Profit \%}{100}\right]\] C.P. = \[S.P.\left[\frac{100}{100 + Profit \%}\right]\]
4	If an object is sold on r% loss, then S.P. = \[\left[\frac{100 - Loss \%}{100}\right]\] C.P. = \[\left[\frac{100}{100 - Loss \%}\right]\]
5	If A sells an article to B at a% profit and B sells it to C at b% profit (OR) If a% and b% are two successive profits, then Total Profit % = \[\left(a+b+\frac{ab}{100}\right)\%\]
6	If A sells an article to B at a% profit and B sells it to C at b% profit and if C paid x, then amount paid by A will be \[A=x\times\left(\frac{100}{100+a}\right)\left(\frac{100}{100+b}\right)\]
7	If a% and b% are two successive losses, then Total Loss % = \[\left(-a-b+\frac{ab}{100}\right)\%\]
8	If a% profit and b% loss occur, simultaneously, then overall loss or profit% is \[\left(-a-b-\frac{ab}{100}\right)\%\]
9	If a% loss and b% profit occur, simultaneously then overall loss or profit% is \[\left(a-b-\frac{ab}{100}\right)\%\]
10	If a% loss and b% profit occur, simultaneously then overall loss or profit% is \[\left(a-b-\frac{ab}{100}\right)\%\]
11	If a% loss and b% profit occur then, total loss/profit is \[\left(-a+b-\frac{ab}{100}\right)\%\]
12	If cost price of ‘x’ articles is equal to selling price of ‘y’ articles, then Selling Price = x, Cost Price = y Hence, Profit or Loss % = \[\frac{x-y}{y} \times 100\]
13	On selling ‘x’ articles the profit or loss is equal to Selling of ‘y’ articles, then Profit % = \[\frac{y \times 100}{x-y}\] Loss % = \[\frac{y \times 100}{x+y}\]
14	If a man sells two similar objects, one at a loss of x% and another at a gain of x%, then he always incurs loss in this transaction and loss % = \[\frac{x^2}{100} \%\]
15	A man sells his items at a profit/loss of x%. If he had sold it for R more, he would have gained/lost y%. Then C.P. of items = \[\frac{R}{\left(y\pm x\right)}\times100\] ‘+’ = When one is profit and other is loss. ‘–’ = When both are either profit or loss.
16	If a man purchases ‘a’ items for x and sells ‘b’ items for y. then profit or loss per cent is given by \[\left(\frac{ay-bx}{bx}\right)\times100\%\]
17	If the total cost of ‘a’ articles having equal cost is x and the total selling price of ‘b’ articles is y, then in the transaction gain or loss per cent is given by \[\left(\frac{ay-bx}{bx}\right)\times100\%\]
18	A dishonest shopkeeper sells his goods at C.P. but uses false weight, then Gain % = \[\left(\frac{\text{True weight - False weight}}{\text{False weight}}\right)\times100\] (OR) Gain % = \[\left(\frac{\text{Error}}{\text{True value - Error}}\right)\times100\]
19	If A sells an article to B at a profit (loss) of r₁% and B sells the same article to C at a profit (loss) of r₂% then the cost price of article for C will be given by C.P of article for C = \[\text{C.P. of A} \times\left(1\pm\frac{r_1}{100}\right)\left(1\pm\frac{r_2}{100}\right)\] (Positive and negative sign conventions are used for profit and loss.)
20	If a vendor used to sell his articles at x% loss on cost price but uses y grams instead of z grams, then his profit or loss% is \[\left[\left(100-x\right)\frac{z}{y}-100\right]\%\] (Profit or loss as per positive or negative sign).