# Arithmetic Aptitude :: Profit and Loss

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## Profit and Loss Important Formulas

Cost Price or CP:
The price at which an article is purchased, is called its cost price, abbreviated as C.P. Cost price is the amount that comes out of the buyer when purchasing any article or a particular item.

Selling Price or SP:
The price at which an article is sold, is called its Selling price, abbreviated as S.P. The selling price is the amount that comes when selling anything.

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 S.P is less than C.P., the seller is said to have incurred a 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 = $$\frac{x}{(100 - x) \times y} \times A$$