Profit and Loss shortcut tricks and concept

As we all know profit and loss question is the very import part of any competitive exam. Math is not hard to study but we need to score more in less time so we need shortcut and tricks to solve them. here we discussed  the shortcut tricks with proper explanation. This will not only make you understand it better but will also let you complete the questions in lesser time. 

Cost Price-The price at which an article is purchased is called its cost price (C.P.)
Selling Price-The price at which the article is sold is called its selling price (S.P.)

Loss = C.P. - S.P.

Gain% = {Gain*100}/{C.P.}
Loss% = {Loss*100}/{C.P.}

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)]
If a cost price of m articles is equal to the selling Price of n articles, then Profit percentage
(m-n)/n×100%

If cost price of 'a' articles is equal to the selling price of 'b' articles, then profit percentage
= (a – b)/b  × 100%
Example If cost price of 20 articles is equal to the selling price of 18 articles, then profit percentage.
Soln. Given that a = 20, b = 18
According to formula,
Profit % = (20 – 18)/18  × 100%
= 2/18  × 100% = 100/9  = 11 1/9 %

If a shopkeeper sells his goods at a% loss on cost price but uses b g instead of c g. then, his percentage profit or loss is
= [ (100 – a) c – 100 ]/b %
As sign positive or negative.
Example If a dealer sells goods at 6% loss on cost price but uses 14 g instead of 16 g. what is his percentage profit or loss?
Soln. Given that a = 6%, b = 14 g, C = 16g
According to formula,
Required answer = [ (100 – 6) 16 – 100 ] %
14
= ( 752 – 700 ) /7% = 52/7 % = 7 3/7 % gain
+ve sign shows that there is a gain. 

A shopkeeper when sells on object for Rs. 900, then he faces loss which is equal to half of the profit gained if the object is sold for Rs. 1200. Find cost price.

C.P. = 900+100  or  1200 - 200

    =Rs 1000










A person sold an article at 12% profit. Had he sold it for ₹ 18. more he would have gained 18%. What is the cost price of the article?

Formula :- SP = CP [ 1 + ( Gain % x 100) ]
for 12 %    SP = CP ( 1 + 0.12) = 1.12 CP
for 18 %  SP = CP ( 1 + 0.18) = 1.18 CP

So the difference  is ₹ 18. i.e 1.18CP – 1.12CP = 18.

CP = 18 / 0.06 = 1800 / 6 = 300. Ans - 300