# Profit and Loss : Important Terms, Formulas, Tips and Tricks

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.