Profit & Loss
Definitions
i)Cost Price :
The price at which an article /thing is bought is called its Cost Price, it is denoted by C.P.
ii) Selling Price :
The price at which an article/thing is sold is called its Selling Price, it is denoted by S.P.
iii) Profit :
When selling price is an article/thing greater than cost price hence Profit .
S.P. > C.P.
hence Profit .
iv) Loss :
When cost price is an article/thing greater than Selling Price hence Loss .
C.P. > S.P.
hence Loss .
Note :- Always count profit or loss on Cast Price .
v) Marked Price :
The price at which mark on an article/thing is called Marked Price .
vi) If an article is sold at a gain of 27% , then S.P. = 127% of C.P.
vii) If an article is sold at a loss of 18% , then S.P. = ( 100 - 18 )% of C.P. = 82% of C.P.
Important Formula
i) C.P. = S.P. - Profit
ii) C.P. = S.P. + Loss
iii) Profit = S.P. - C.P
iv) Loss = C.P. - S.P.
Profit X 100
v) Profit % = ------------------
C.P.
Loss X 100
vi) Loss% = -------------------
C.P.
100 X S.P.
vii) C.P. = -----------------
100 + profit%
100 X S.P.
viii) C.P. = ------------------
100 - Loss%
C.P. (100 + Profit )
ix) S.P. = --------------------------
100 + profit%
C.P. (100 - Loss )
x) S.P. = ---------------------------
100 + Loss%
( S.P. - C.P. ) X 100
xi) Profit % = --------------------------
C.P.
(C.P. - S.P. ) X 100
xii) Loss% = --------------------------
C.P.
1) Rule :
Profit = S.P. - C.P.
Example :
Ram buy one pen cost Rs. 100 , he sell it at Rs. 200 . What will be Profit ?
Solution :
Profit = S.P. - C.P.
= 200 -100
= 100
2) Rule :
Loss = C.P. - S.P.
Example :
Ram buy a cow in cost Rs 200 , he sell it at Rs 150 . What will be Profit /loss ?
Solution :
C.P.>S.P. hence loss then
Loss = C.P. - S.P.
= 200 - 150
= 50
3) Rule :
S.P. - C.P.
Profit % = ----------------X 100
C.P.
Example :
Dipika buy a pen cost Rs. 100 , she sell it at Rs 150 . What will be Profit /loss% ?
Solution :
S.P. > C.P. hence Profit then
S.P. - C.P.
Profit% = -----------------X 100
C.P.
150 - 100
Profit% = ---------------X 100
100
= 50%
4) Rule :
C.P. - S.P.
Loss % = -----------------X 100
C.P.
Example :
Ram buy a cow in cost Rs 200 , he sell it at Rs 150 . What will be Profit /loss% ?
Solution :
C.P.>S.P. hence loss then
Loss = C.P. - S.P.
= 200 - 150
= 50
C.P. - S.P.
Loss % = -----------------X 100
C.P.
50
Loss % = ----------X 100
200
= 25%
5) Rule :
We sell one article at P% Profit if C.P. is x then
100 + P%
S.P. = ---------------X x
100
Example :
Riti sell one Pen at Profit 25% if C.P. is Rs. 280 then S.P.
Solution :
100 + 25
S.P. = -------------X 280
100
125
S.P. = -------X 280
100
= 350
6) Rule :
We sell one article at L% Loss if C.P. is x then
100 - L%
S.P. = ---------------X x
100
Example :
Riti sell one Pen at Profit 20% if C.P. is Rs. 200 then S.P.
Solution :
100 - 20
S.P. = -------------X 200
100
80
S.P. = -------X 200
100
= 160
7) Rule :
We sell one article at P% Profit if S.P. is x then
100
C.P. = ----------------X x
100 + P%
Example :
Riti sell one Pen at Profit 20% if S.P. is Rs. 600 then C.P.
Solution :
100
C.P. = ----------------X x
100 + P%
100
C.P. = ----------------X 600
100 + 20
= 500
8) Rule :
We sell one article at L% Loss if S.P. is x then
100
C.P. = ---------------X x
100 - L%
Example :
Riti sell one Pen at Loss 20% if S.P. is Rs. 600 then C.P.
Solution :
100
C.P. = -------------X 600
100 - 20
100
C.P. = -------X 600
80
= 750
9) Rule :
We sell any article on Rs x to get Loss L% , what S.P. to get Profit P%
100 + P%
S.P. = ----------------X x
100 - L%
Example :
We sell cap on Rs 360 to get Loss 10% , What S.P. to get profit 20% .
Solution :
100 + P%
S.P. = ----------------X x
100 - L%
100 + 20%
S.P. = ----------------X 360
100 - 10%
120
S.P. = ---------X 360
90
= 480
Problem on Discount :
Remarks :
1) List price is called the marked price of the article .
2) Discount is reckoned on the marked price .
Example :
1) If the marked price of an article is Rs. 380 and a discount of 5% is given on it, what is the selling price ?
Solution :
95
S.P. = -------X 380
100
= 361
2) If 12% is allowed as discount on a radio and its selling price is Rs. 836, What is its marked price ?
Solution :
Let marked price be Rs. x. Then,
88% of x = 836
100
x = 836 X ----------
88
= 950
Exercise :
1) By selling 12 oranges for a rupee, a man loses 20% . How many for a rupee should he sell to gain 20 % ?
a) 15 b) 10 c) 8 d) 5
2)A man sells two commodities at the same price. On one he gain 20% and one loses 20% on the other . He gets :
a) 1% loss b) 4% loss c) 1% gain d) 0% gain or loss
3) A person sold two shops each for Rs. 9900. If he gained 10% on one and lost 20% on the other , then which one of the following is true ?
a) He gained Rs. 200 b) He lost Rs. 200 c) He neither gained nor lost d) None of these
4) A vendor buys oranges at Rs. 2 for 3 oranges and sells them at a rupee each . To make a profit of Rs. 10 , he must sell :
a) 10 oranges b) 20 oranges c) 30 oranges d) 40 oranges
5) If the selling price of 12 articles is equal to the cost price of 15 articles, the gain per cent is :
a) 25% b) 20% C) 35% D) 75%
Answer :
1) c 2) b 3) d 4) c 5) a
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