# Profit and Loss

Pratice Profit and Loss Questions and answers.

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).