Profit and Loss: 14 Important
Shortcuts & Tricks Explained
Profit and loss problems are
frequently asked problems in competitive exams. Profit and loss is the branch
of basic mathematics which deals with the study of profit and loss made in a
business transaction. The profit and loss account is fundamentally a summary of
the trading transactions of a business and shows whether it has made a profit
or loss during a particular period of account. Indeed, by deducting the total
expenditure from total income the profit or loss of a business can be
calculated. Along with the balance sheet, it is one of the key financial
statements that make up a company's statutory accounts. Basically, this type of
account shows the following information for a business:
a) Sales revenue
earned by business
b) Cost of sales
that the business has incurred
c) Other operating
costs incurred by the business
d) Profit/Loss
earned by business.
Profit and loss is mainly used
in finance and business transactions. Some important profit and loss formulas
are: Notations used in profit and loss: S.P. – Selling price C.P. – Cost price
M.P. – Marked Price.
Points to remember
:
* To find profit or loss when
cost price and selling price are given.
(i). When Selling Price >
Cost Price, There is a Profit and it is given by Selling Price - Cost Price.
(ii). When Selling Price <
Cost Price, There is a Loss and it is given by Cost Price - Selling Price.
* The Profit or Loss is
generally reckoned as so much per cent on the cost.
Gain or loss per cent
=
( Loss or Gain / CP )× 100
* C.P in terms of S.P
and P%
C.P = [ (S.P *100)/(100+P%) ]
* C.P in terms of S.P
and L%
C.P = [ (S.P *100)/(100-L%) ]
* S.P in terms of C.P
and P%
S.P = [ C.P*(100+P%)/100 ]
* S.P in terms of C.P
and L%
S.P = [ C.P*(100-L%)/100 ]
Some shortcuts :
Trick-1:
If persons sells two same
items one at profit of x%, another at x% of loss.then, always loss occurs given
by
Loss % = (square of x)/10
Trick-2:
If a trader uses false weight.then
Profit% =
[True weight - false weight /
false weight ]*100
Ex:A shopkeeper professes to
sell his goods at cost price but uses a weight of 800gm instead of 1kg. thus he
makes a profit of?
a. 20% b. 16.2/3
c. 25 d. 50
Sol : ( 200/1000-200)*100 = 25
%
Trick-3:
If cost price of P articles is
equal to selling price of Q articles [P>Q].then,
Profit% =
[ (P-Q)/Q ] * 100
Trick-4:
If a person marks his P% above
the cost price and offers a discount of Q%.then,
Profit% or Loss%
= [ P - Q - ( P * Q
)/100 ]
Trick-5:
If there are two successive
profits R1% and R2%.then,
Profit% = [R1 + R2 + (
R1*R2)/100]
Trick-6:
If there are profit R1%
and loss R2%.then,Total Profit%
or Loss%
= [R1 - R2
- ( R1*R2)/100]
Trick-7:
i. If P sells an item to Q at
profit of R1%. then, Q sells that item to R at profit of R2%. Then, R sells
that item to S at profit of R3%. Then, cost price of S is
= (Cost price of P)*(1+R1/100)
*
(1+R2/100)* (1+R3/100)
ii. If P sells an item to Q at
loss of R1%. then, Q sells that item to R at loss of R2%. Then, R sells that
item to S at loss of R3%. Then, cost price of S is
= (Cost price of P)*(1-R1/100)
*
(1-R2/100)* (1-R3/100)
ii. If P sells an item to Q at
profit of R1%. then, Q sells that item to R at loss of R2%. Then, R sells that
item to S at profit of R3%. Then, cost price of S is
= (Cost price of P)*(1+R1/100)
*
(1-R2/100)* (1+R3/100)
Note:if he sells at loss.
Then, Represented by ' - ' .he sells at profit. Then, Represented by ' + '
Trick-8:
If the profit earned by
selling a painting for Rs x is equal to the loss incurred when the same
painting is sold for Rs y, then to make z% profit the sale price of the
painting should be
Rs [ (x + y)(100
+ z) ] * 200
Trick-9:
If a reduction of x % in the
price of rice enables a person to buy n kg more for Rs A, then the reduced
price per kg of the rice are
[ (A*x)/( 100 - n ) ]per kg
and original prices per kg of the rice are
[ (A * x)/( 100 - n) * x ] per
kg
Trick-10:
If 'a' articles are bought for
Rs 'b' and sell them 'c' articles for Rs 'd'. Then profit or loss made by the
vender:
[[(a*d) - (b*c)] /b*c ]*100
Trick-11:
If a object sold at X then L%
loss occured,inorder to get P% profit.The object has to sold at
=[ (100 +
P)/( 100 - L )] * ( selling price at L%)
Trick-12: The ratio of the cost price and the selling price is m:n. The profit or
loss percent is
Profit% = [ ( m-n )/m
]*100
Loss% = [ ( n-m)/m
]*100
Ex: The ratio of the cost
price and the selling price is 4:5. The profit percent is?
a. 10 b.
20 c. 25 d. 30
Sol: Profit% = [( 5-4 )/4]*100
= 25%
Trick-13:
If on selling 'm' notebooks a
seller makes a profit ( if loss )equal to selling price of 'n' notebook, the
profit percentage is
=
[ n/(m-n) ] * 100
Loss percentage is
=
[ n/(m+n) ] * 100
Ex: If on selling 12 notebooks
a seller makes a profit equal to selling price of 4 notebook, what is his
profits percentage?
a. 16.2/3 b. 25 c. 50 d. None
of these
Sol : P% = [ 4 /(12-4) ]*100 =
50%
Trick-14:
Some article were brought of m
for rs. n. And sold at n for rs. m. Gain percentage is (m > n)
= [[
(m*m)-(n*n) ]/(n*n)]*100
Ex:Some article were brought
of 6 for rs. 5. And sold at 5 for rs. 6. Gain percentage is?
a. 30. b. 33.1/3
c. 35 d. 44
Sol: [ (36-25)/25 ]*100 = 44% for more click here
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