Profit, Loss And Discount – Examples And Tricks To Solve

In the case of profit or loss, the relation is generated between c.p and s.p 

If 25% profit accrued on an article it means :

100% represents cost price (c.p)
125% represents selling price (s.p)
25% represents profit
i.e. ( 25 % => 125 % (s.p) )
( => 100 % (c.p) )

If 15% loss accrued on an article , it means:
100% represents cost price (cp)
85% represents selling price (sp)
15 % represents loss
i.e ( 15 % => 100 % (c.p) )
( => 85 % ( s.p) )

In the case of discount the relation is generated between sp and mp

If 20% discount accrued on an article its means :
100% represent the marked price (mp)
80% represent the selling price (sp)
20% discount
i.e ( Discount 20 % => 100 % (mp) ) ( =>(100 – 20 % discount = 80 % (s.p) )

Example: A person purchased an article for Rs 120 and sold it for Rs 150 . Find his % profit.

Sol. c.p of the article = Rs 120
s.p of the article = Rs 150

Profit of the person = 150 – 120 = 30

% profit of the person ( = { Profit over (cp)} times 100 )

% profit (= {30 over 120} times 100 )
= 25% (Answer)

Example: A dishonest shopkeeper sells goods at his cost price but uses a weight of 425 gm instead of 500g. Find his gain percent.

Sol. The c.p of shopkeeper = 425gm
The s.p of shopkeeper = 500gm

The profit of shopkeeper = 500 – 425 = 75 gm

% profit of shopkeeper = ( {Profit of shopkeeper over c.p of shopkeeper} times 100 )

( = {75 over 425} times 100 )

( % Profit = 17 {11 over 17} ) (Answer)

Example: A person got 5% loss by selling an article for Rs 1045 . At what price should the article be sold to earn 15% profit ?

Sol. Let the new s.p be Rs x then
({100 – Loss % over 1st s.p} = {100 + gain % over 2nd s.p} )

( = {(100-5) over 1045}={(100+15) over x} )

( x = {115 times 1045 over 95} )

= Rs. 1265 (answer)

[ short trick:]

New ( sp = {1045 over 95} times 115 = 1265 )

Example: A person sold an article at profit of 15% if he had sold it at Rs 480 more, he would have gain 18% what is the cost price ?

Sol. Let the c.p of an article be x Rs then ,
=> 115% of x + 480 = 118% of x

=> 118% of x – 115% of c = 480

=> 3 % of x = 480
( x = {480 over 3} times 100 )

= Rs 16000 (answer)

[short trick:]
( cp = {Difference in sp over diffrence in profit %} times 100 )

( cp = {480 over 3} times 100 )

= Rs. 16000 (answer)

Example : find the equivalent discount of 10% and 20% .

Sol. Let the MP be = Rs 100

Then net ( sp = 100 times {90 over 100} times {80 over 100} )

= Rs 72
Required discount = (100 – 72)%
= 28% (Answer)

[short trick:]

( X + Y- {xy over 100} )

( 10+20-{10 times 20 over 100}

= 28 % )