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:]
\( X + Y- {xy \over 100} \)
\( 10+20-{10 \times 20 \over 100} = 28 \% \)