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 % )