Hi Reader, Today we will deal with a Profit and Loss which is a very crucial topic of all competitive exams.

**Important Terms Used to Solve Profit and Loss :**

**Cost Price ( CP ) :**The price at which an article is purchased is called its cost price.

**Selling Price ( SP ) :**The price at which an article is sold is called its selling price.

**Profit or Gain :**If the selling price of an article is greater than its cost price, then the shopkeeper makes a profit ( or gain ).

**Loss :**If the cost price of an article is greater than its selling price, then the shopkeeper suffers loss.

**Marked Price ( MP ) :**The price which is printed on an article is called marked price.

**Discount :**The concession given on marked price of any product is called discount.

**Basic Profit and Loss Formulas :**

**Profit**= Selling Price - Cost Price

**Loss**= Cost Price - Selling Price

**Profit %**= 100 ( Profit / Cost Price )

**Loss %**= 100 ( Loss / Cost Price )

**Selling Price**= Cost Price [ ( 100 + Gain % ) / 100 ]

**Selling Price**= Cost Price [ ( 100 - Loss % ) / 100 ]

**Cost Price**= Selling Price [ ( 100 / ( 100 + Gain % ) ) ]

**Cost Price**= Selling Price [ ( 100 / ( 100 - Loss % ) ) ]

**Some Important Profit and Loss Cases :**

If a person sells two similar articles, one at a gain of a% and another at a loss of a %, then the seller always incurs a loss which is given by Loss % =

**( a / 10 ) ^ 2**
If a'th part of some items is sold at x % loss, then required gain per cent in selling rest of the items in order that there is neither gain nor loss in whole transaction, is

**( a x ) / ( 1 - a )**
If a dishonest trader professes to sell his items at cost price but uses false weight, then

**Gain % = ( Error ) 100 / ( True Value - Error )**

**Gain % = [ ( True weight - False weight ) / ( False weight ) ] 100**

If a shopkeeper sells his goods at a % loss on cost price but uses b g instead of c g, then his profit or loss % is

**[ ( 100 - a ) ( c / b ) - 100 ]****Note :**If resultant come +ve then there will be overall profit . if it come -ve then there will be overall loss.

If a dealer sells his goods at a% profit on cost price and uses b% less weight, then his percentage profit will be

**[ ( b + a ) / ( 100 - b ) ] 100**
If 'a' part of an article is sold at x % profit / loss, 'b' part at y % profit / loss and c part at z % profit / loss and finally there is a profit / loss of Rs.R, then cost price of entire article =

**( 100 R ) / ( a x + b y + c z)**
When there are two successive Profit of x % and y % then the resultant profit per cent is given by

**[ x + y+ ( x y / 100 ) ]**
If there is a Profit of x% and loss of y % in a transaction, then the resultant profit or loss% is given by

**[ x - y - (x y / 100 ) ]****Note :**For profit use sign + in previous formula and for loss use - sign. If resultant come +ve then there will be overall profit . if it come -ve then there will be overall loss.

If a cost price of m articles is equal to the selling Price of n articles, then Profit percentage

**[ ( m - n ) / n ] 100**
A man purchases a certain no. of article at m a rupee and the same no. at n a rupee. He mixes them together and sold them at p rupee then his gain or loss % is given by

**[ { 2 m n / ( m + n ) p } -1 ] 100****Note :**If resultant come +ve then there will be overall profit . if it come -ve then there will be overall loss.

When a person sells two similar items, one at a gain of say x%, and the other at a loss of x %, then in this transaction the seller always incurs a loss given by

**{ x ^ 2 / 100 }**
A single discount equivalent to discount series of x% and y% given by the seller is equal to

**(x +y - x y / 100) %**
If a seller marks his goods at x% above his cost price and allows purchasers a discount of y % for cash, then overall gain or loss

**( x - y - x y / 100 ) %****Note :**If resultant come +ve then there will be overall profit . if it come -ve then there will be overall loss.

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