# Arithmetic Aptitude :: Profit and Loss

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**Important Formulas**

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**Profit and Loss Important Formulas**

**Cost Price or CP:**The price at which an article is purchased, is called its

*abbreviated as*

**cost price,***Cost price is the amount that comes out of the buyer when purchasing any article or a particular item.*

**C.P.****Selling Price or SP: **The price at which an article is sold, is called its

*abbreviated as*

**Selling price,***The selling price is the amount that comes when selling anything.*

**S.P.****Profit or Gain: **If S.P. is greater than C.P., the seller is said to have a profit or profit.

**Profit = SP – CP**

**Loss: **If

**is less than**

*S.P***the seller is said to have incurred a**

*C.P.,*

**loss.****Loss = CP – SP**

Note:**Profit** and **Loss** is always calculated on **Cost Price** or **CP**.

What is the formula of Profit percentage?

Profit% = \(\left[\frac{Profit \times 100}{C.P.}\right]\)%

OR

Profit percentage formula can be:

Profit% = \(\left[\frac{\left( S.P. - C.P. \right) \times 100}{C.P.}\right]\)%

What is the formula of Loss percentage?

Loss% = \(\left[\frac{Loss \times 100}{C.P.}\right]\)%

OR

Loss percentage formula can be:

Loss% = \(\left[\frac{\left( C.P. - S.P. \right) \times 100}{C.P.}\right]\)%

If a shopkeeper sells an article of cost price (C.P) ad there is a Profit in %, then the selling price of the article (C.P.).

S.P. = \( \left[\frac{100 + Profit% }{100} \times C.P. \right]\)

If a shopkeeper sells an article of cost price (C.P) ad there is a Loss in %, then the selling price of the article (C.P.).

S.P. = \( \left[\frac{100 - Loss% }{100} \times C.P. \right]\)

If a shopkeeper sells an article on S.P. (S.P.> C.P.) and there is a Profit in %, then the cost of the article (C.P.).

C.P. = \( \left[\frac{100}{100 + Profit% } \times S.P. \right]\)

If a shopkeeper sells an article on S.P. (S.P.< C.P.) and there is a loss in %, then the cost of the article (C.P.).

C.P. = \( \left[\frac{100}{100 - Loss% } \times S.P. \right]\)

If an article is sold at a profit of say, 35%, then S.P. = 135% of C.P.

If an article is sold at a loss of say, 35%, then S.P. = 65% of C.P.

**Dishonest Seller:**

A dishonest seller claims to sell his goods at cost price, but he uses lesser weight to weight his goods.Find his gain%.

Gain/Profit% = \(\left[\frac{true \ weight \ - \ false \ weight}{false \ weight} \times 100 \right]\)

A shopkeeper sells his good at a profit of x % and uses a weight which is y% less to the original weight. Find his total profit.

Gain/Profit% = \(\left[\frac{Profit\ percentage + Less \ in \ weight}{100 \ - \ less \ in \ weight} \times 100 \right]\)

**Two successive profits:**

When there are two successive profits of suppose x% and y% then there will be always profit and the net percentage profit = \(\left[\frac{x \ + \ y \ + \ xy}{100}\right]\)

**profits & Loss OR Loss & Profit:**

When there is a profit of supose x% and loss of y% then net percentage profit or loss = \(\left[\frac{x \ - \ y \ - \ xy}{100}\right]\)

**Note: ** If the last sign in the above expression is positive then there is net gain but if it is negative then there is net loss.

A sells goods to B at a profit of x% and B sells it to C at a profit of y%. If C pays **Rs P** for it, then the cost price for A is:

Cost price for A = Rs.\(\left[ \frac{100 \times 100 \times P}{(100 \ + x)(100 \ + y)}\right]\)

**Note:** If in case there is loss replace plus sign with negative sign.

If the price of a commodity increases by R%, then what should be the reduction in consumption, so that the expenditure remains the same:

reduction in consumption % = \(\left[\frac{R}{100 \ + R} \ time 100\right ]\)%

If the price of a commodity decreases by R%, then what should be the increase in consumption, so that the expenditure remains the same:

increase in consumption % = \(\left[\frac{R}{100 \ - R} \ time 100\right ]\)%

A reduction of x% in price enables a person to buy y kg more for Rs.A. Then the

Reduction in price = \(\frac{x}{100 \times y} \times A \)

Original price = \(\frac{x}{(100 - x) \times y} \times A\)