1.
PERCENTAGE is one of the most commonly used
mathematical concept in real life. This is simple
concept with various concept with various
applications. Hence, you are expected to be
absolutely confirm with this concept. In order to
increase your confirm levels, you will do well to keep
calculating percentages mentally, whenever you get
an opportunity to do so in real life
PERCENTAGE

2.
PERCENTAGE OF A NUMBER
 Percent means, per 100. here “cent” stand for
100 .
To find the percentage of a number, convert the
%age into fraction and multiply the resulting
fraction with the number,
e.g. 60% of 500 = 60
100

3.
CONVERSION OF A FRACTION OR
A DECIMAL INTO A PERCENT
A fraction or decimal can be converted in
to a percentage by simply multiplying it
by 100.
so, the fraction 1/5 expressed as a
percentage is 1/5*100 = 20%
And the decimal 0.05 expressed as a
percentage is 0.05 * 100 = 5%

4.
Converting a percentage into a
fraction
 A %age when divide by 100 is converted into a
fraction. So 20% as a fraction is 20/100 = 1/5
The % sign is dropped when we divide the % by
100.
Fraction of a number
 To determine the fraction of a number we multiply
the fraction and the number. Therefore,

5.
Fraction of a fraction and relative
percentage
 To find the fraction of a fraction we multiply both
the fractions.

6.
Type of questions Examples
If A’s income is
x% of B’s income
and B’s income is
given. Then find
A’s income.
A’s income is
40% of B’s
income. If B’s
income is
Rs.10,000, what is
A’s income?

7.
Approach

8.
Type of questions Examples
If A’s income is r%
more than of B’s
income, than by
how much
percent is B’s
income less than
A’s income?
X’s income is 25%
more than Y’s. By
how much % is
Y’s income less
than X’s income?

9.
Approach

10.
Type of questions Examples
Approach
If A’s income
is r% less
than of B’s
income, than
by how much
percent is B’s
income more
than A’s
income?
X’s income is
20% less than
Y’s. By how
much % is Y’s
income more
than X’s
income?

11.
Approach

12.
Type of questions Examples
If A’s income is r%
less than of B’s
income, than by
how much percent
is B’s income more
than A’s income?
X’s income is 20%
less than Y’s. By
how much % is Y’s
income more than
X’s income?

13.
Approach

14.
Type of questions Examples
If the price of a
commodity
increases by r%,
find the % decrease
in the consumption
given that
expenditure remain
same
If the price of potato is
increased by 20%, by how
much should the
consumption be decreased
so as to maintain the same
expenditure?

15.
Approach

16.
Type of questions Examples
If price of one unit
changes by a% and
the number of units
consumed changes
by b%, than what is
the % change in
expenditure
If the price of potato is
increased by 20% and
consumption
decreased by 10%,
what will be the
percentage change in
expenditure?

17.
Approach

18.
Type of questions Examples
1. If the population of a
country increases in the
first year and decreases
in second year.
The population of a town is
18,000.
It increases by 10% during
first year and by 20%
during the second year. The
population after 2 years
will be

19.
Approach

20.
Alternative Method
Successive increments of 10%
and 20% = 32%.
Then, population will increase
by 32% of 18000 = 5760
population after 2 years will be
18000+5760 = 23760

21.
EXAMPLES:-
 A’s income is 70% of B’s income. B’s income
is 50% of C’s income. If C’s income is Rs. 1,
00,000. What is A’s income?
 If the price of an item is increased by 20%
and then a discount of 10% is given on the
increased price, what will be the effect on
sale?
 The number of seats in an auditorium is
increased by 25%. The price on a ticket is
also increased by 12%. What is the effect on

22.
 The length of a rectangle is increased by 10%. What will be the
percentage decrease in its breadth so as to have the same area?
 In a market survey, 20% opted for product B. The remaining
individuals were uncertain. If the difference between those who
opted for product B and those who were uncertain was 720, then
how many individuals were covered in the survey?
 Of the total amount received by Kiran, 20% was spent on
purchases and 5% of the remaining on transportation. If he is left
with Rs. 1520, the initial amount was
 5% of income A is equal to 15% of income B and 10% of income
B is equal to 20% of income C. if income of C is Rs. 2,000 , then
the total income of A, B and C is

23.
 Arvind spend 75% of his income. His income is increase by 20%
and he increases his expenditure by 10%. His saving is increased
by how many percent?
 Two numbers are respectively 19% and 70% more than a third
number. What percentage is the first number out of the second?
 Salary of A, B and C are in the ratio of 1:2:3. Salary of B and C
together is Rs. 6,000. By what percent is the salary of C more
than that of A?
 The price of rice increased from Rs. 15 by 15% and then reduce
by 30 paise. What was the net increase?
 Successive discount of 30%, 20% and 10% are equivalent to a
single discount of?

24.
 SUPPOSE that you are selling some
article. You can sell that article at the
price you bought, more than that or less
than that, means in any such transaction
three cases will be arise
PROFIT, LOSS AND DISCOUNT

25.
THEORY AND CONCEPT
 In day to day life we sell and purchase the
things as per our requirement. A customer can
get things in the following manners:
Manufacturer
(or producer)
Whole seller
(dealer)
(shopkeeper)
Retailer
(or sells
person)
Customer

26.
TERMINOLOGY
 COST PRICE – The money paid by the
shopkeeper to the manufacturer or whole
seller to buy the goods is called the cost
price(CP) of the goods purchased by the
shopkeeper.
 Selling Price (SP) – The price at which the
shopkeeper sells the goods is called the
selling price (SP) of the goods sold by the
shopkeeper.
NOTE- If an article is purchased for some amount and
three are some additional expenses or transportation
labor, commission etc., these are to be added in the
cost price. Such expenses are called overhead
expenses or overheads.

27.
a. Cost price (C.P.) > selling price (S.P.)
b. Cost price (C.P.) < selling price (S.P.)
c. Cost price (C.P.) = selling price (S.P.)
as a result either you will have profit (p)
or loss (L) or no profit or no loss

28.
Profit & Loss can be defined in two
ways
A. In term of absolute amount:
suppose that if CP of an article is Rs.200 and
SP is 300.
so profit is SP-CP = 300-200 = 100.
B. In terms of percentage:
wherenever you want to calculate the prpofit &
loss in terms of percentage, it is always
calculated on the basic of CP. In the above
example the profit is Rs. 100on CP of 200, so
the profit % is 50%

29.
IMPORTANT FORMULAE
Profit = SP-CP
Loss = CP – SP
Profit percentage =

30.
NOTE – Profit & loss is always calculated on the basic of cost price
unless otherwise mentioned in the problems

31.
MARK UP AND DISCOUNT
MARKED PRICE – Basically to avoid the loss
due to bargaining by the customer and to get
the profit over the cost price trader increases
the cost price by a certain value, this increase
in the value over cost price is known as
markup and the increase price is called the
marked price or printed price or list price in
the goods.
Marked price = CP+ Markup
Marked Price = CP +(% markup on CP)

32.
Discount : discount means reduction of marked
price to selln at a lower rate or literally discount
means concession. Basically it is calculated on the
basic of marked price.
Selling price = marked price – discount
Selling price = Marked price – ( discount % on MP)

33.
Since markep price = CP+ % markup on CP
remember markup is calculated on the basic of CP
while discount is calculated on the basis on MP
in general, CP>SP<MP at profit
CP=SP<MP at no profit no loss
SP<CP<MP at loss

34.
Type of questions Examples
1. If A sells to B at a profit
of x%;
B sells to C at a profit of
y%
and C pays Rs. P for it,
find the cost for A.
A sells a cycle to B at a
profit of 10%, B sells to C
at a profit of 20%. If C pays
Rs. 264 for it, how much
did A pay for it?

35.
Type of questions Examples
1. If cost price of A articles
is equal to the selling
price of B articles, find
the profit percentage.
The cost price of 10
articles is equal to the
selling price of 9 articles.
Find the profit percentage.

36.
Type of questions Examples
1. The cost price of two
articles is same. If one is
sold at a X% profit and
the other at a loss of X
%, find the profit or loss
percentage.
Amit buys 2 cows for Rs.
200 each. He sells one at a
profit of 10% and the
other at a loss of 10%. Find
his profit or loss
percentage.

37.
Approach
For the equal profit & loss %age, there is no
profit no loss

38.
Type of questions Examples
1. The selling price of two
articles is same. If one is
sold at a X% profit and
the other at a loss of X
%, find the profit or loss
percentage.
Amit sells 2 cows for Rs.
200 each. On one he gets a
profit of 10%, while losing
10% on other. What is his
overall profit or loss
percentage?

39.
Approach
For the same selling price & equal profit &
loss percentage there is always a loss of

40.
Type of questions Examples
1. If x % discount on an articles
is given on cash payment.
Find the %age that should be
marked above the cost price
so as to make a profit of y%.
A dealer allows a discount of
7% for cash payment. How
much %age above the cost
price should he marks his
goods to make a profit of 10%

41.
Approach

42.
Type of questions Examples
1. If a dealer sells goods at
cost price but uses faulty
weight, find his gain
percentage.
A dishonest dealer
professes to sells to sell his
goods at cost price, but he
uses weight of 960 gm for
1 kg. find his profit %age.

43.
Approach

44.
EXAMPLES :-
 A boy buys eggs at 10 for Rs. 1.80 and sells them at
11 for Rs. 2. What is the profit or loss %?
 a man bought 80 kg of rice for Rs. 88 and sold it at a
loss of as much money he received for 20 kg. At what
price did he sell it?
 goods are purchased for Rs. 450 and one-third is sold
at a loss of 10%. At what profit %age should the
remainder be sold so as to gain 20 % on the whole
transaction?

45.
a reduction of 10% in the price of sugar enables a man to buy
25 kg more for Rs. 225. What is the original price of sugar?
a man sells an articles at a profit of 25%. If he had bought it
at 20% less and sold it for Rs. 10.50 less, he would have
gained 30%. Find the C.P. of the articles.
if a commission of 10 % is given on the marked price of an
articles, the gain is 25%. Find the gain %age, if the
commission is increased to 20%.
peanuts are sold at 60 per rupee. If the vendor decides to
hike the S.P. by 20%, how many peanuts can be bought per
rupee?

46.
 Sumeet buys 9 books for Rs. 100 but sells 8 for Rs.
100. What is the next %age of profit?
 A person earns 15% on an investment but losses 10%
on another investments. If the ratio of two investments
be 3 : 5, what is the gain or loss on the two
investments taken together?
 Vivek purchased 120 tables at a price of Rs. 110 per
table. He sold 30 tables at a profit of Rs. 12 per table
and 75 tables at a profit of Rs. 14 per table per table.
The remaining tables were sold at a loss of Rs. 7 per
table. What is the average profit per table?