PERCENTAGE AND IT'S
APPLICATIONS
1 3 32
You are already acquainted with the fractions. For example, , , , . . . etc.
3 8 35
are fractions. You have also learnt that for comparing two or more fractions. we express
them in the form of equivalent fractions, so that their denominators are equal. A fraction
whose denominator is 100 is called percent.
From this lesson, you will learn:
• Writing percent in the form of fraction
• Writing a fraction in the form of percent
• Solving questions based on percentage
• Solving profit and loss questions through the application of percentage
• Solving Discount related questions based on percentage
8.1 Fractional form of percent
Let us learn how to write a fraction in the percent form and write the percent into
fractions. To understand this let us take some examples:
Example 8.1
3 2
Compare and
8 7
3 2
We have to write & in the form of equivalent fractions such that the
8 7
denominator is the LCM of their denominators
LCM of 8 & 7 is 56
Hence
3 3 7 21
=
8 8 7 56
2 2 8 16
= =
7 7 8 56
21 16
Here we see that
56 56
3 2
87
Example 8.2
9 4
Compare and
10 50
9 41
Fractions are &
10 50
9 9 5 45
= =
10 10 5 50
41 41
=
50 50
45 41 9 41
Now > >
50 50 10 50
For converting the fractions into percent we need to make denominator as 100
9 9 10 90 41 41 2 82
10 = 10 10 = 100 , also 50 = 50 2 = 100
90 82 9 41
Here also > >
100 100 10 50
90% and 82% 90% is more them 82%
8.1.1 To convert fractions into percent
90 90 1
In the above example you have seen that is 90% we write as 90×
100 100 100
1
100 represents%
1
90× 100 = 90%
82 1 1
Similarly = 82 × 100 = 82% 100 is %
100
To convert a fraction into percent, we have to make the denominator as 100.
Hence we multiply numerator & denominator by the same number so that denominator
becomes 100. In case we donot get 100, then we multiply the denominator and
numerator by 100 but denominator should remain, 100 numerator can be simplified.
Example 8.3
Write the following fractions into percent
3 7
(i) (ii) 1 (iii) 0.7
5 15
3 3 20 60 1
Sol. (i) = = = 60 × = 60%
5 5 20 100 100
7 22 20 440 440 1 440
(ii) 1 = = = × = 3 %
15 15 20 300 3 100
2
or 146 %
3
7 7 10 70 1
(iii) 0.7 = = = = 70× = 70%
10 10 10 100 100
Example 8.4
Write the following % in to fraction
2
(i) 45% (ii) 16 (iii) 11.5%
3
1 45 9
45% = 45× = = (Dividing numerator and denominator by 5)
100 100 20
2 50 50 1 50 1
(ii) 16 % = %= × = =
3 3 3 100 300 6
1 23 1
(iii) 11.5% = 11.5× = ×
100 2 100
23
=
200
Example 8.5
(i) 160 is what percent of 200?
(ii) 3.5 kg is what percent of 25 kg
80
160 100
Sol. (i) Required% = 200 = 80%
Another method 160 is out of 200 then out of 100 will be half of 160 or 80
(ii) Required percent of 25kg for 3.5kg
3.5
25 100 % {Here we are multiplying by 100, as we are to find how
much out of hundred}
7 35 2
100
= 250
5
= 14%
Intext Questions 8.1
1. Write the following fractions into percent
15 5 1 3
(i) (ii) (iii) 0.68 (iv) 1 (v)
20 6 4 25
2. Write the following percent into lowest form fraction
2 1
(i) 15% (ii) 66 (iii) 13 %
3 3
3
(iv) 35% (v) 23 %
4
3. (i) What percent of 180 is 90?
(ii) What percent of ` 75 is ` 45?
(iii) What percent of 50 is 15 litre?
8.2 Find out a specific percent of a given amount
Let us take some examples to explain how we find the given percent of an
amount
Example 8.6
(i) Find 15% of ` 1500
(ii) Find 45% of 250kg
Sol: (i) 15% of ` 1500
1
= 15 00 15 100 = ` 225
(ii) 45% of 250kg
1
5
= 250 45 100 kg
2
225
= kg
2
1
= 112 kg
2
Example 8.7
If 25% of the length of a line segment is 6 meter, then find out the length of the
line segment.
Sol. Out of 100 is = 25 or say if 25m length of line segment then total
length = 100
25
Out of 1 is = 100
100 If 1m length then the total length =
25
25
Out of x is = x 100
100 If 6m length then the total length = × 6 = 24m
25
25 x
100 = 6
x = 6× 100 4
25
Required length = 24 meter
Intext Questions 8.2
1. Find the value of the following
(i) 26% of 25 litre (ii) 75% of 40kg (iii) 20% of ` 1900
2. Find the value of x in the following
(i) 16% of x is 260
(ii) 1.5% of x is ` 108
(iii) 90% of x is 216km
8.2.1 Some word problems based on percentage
Example 8.8
There are 1300 trees in a garden. Out of them 26% are Guava trees. What is
the number of rest of the trees?
Sol. Total no. of trees = 1300
26
No. of Guava trees = 1300 100 = 338
No. of rest of trees = 1300 –338 = 962 trees
Example 8.9
The monthly income of a person is ` 16,000, out of this he spends ` 12000.
What percent of his income does he save?
Sol. The amount of saving = Total income –expenditure
= ` (16000–12000)
= ` 4000
Saving in the form of percent
4 000
= 16 000 100 %
= 25%
Example 8.10
Find the amount which becomes ` 1331 after 10% increase.
Sol. Let the required amount = ` x
Hence x + (10% of x)
x 11x
=x+ =
10 10
11x 1331 10
Give = 1331 x = x = `1210
10 11
Required amount = ` 1210
Example 8.11
In a particular year there is a 150% increase in the enrolment. If in the begining
there were 1500 students, then find the students after enrolment.
Sol. No of students in the begining = 1500
15
Increase = 1500 ×
100
15 15
= ×
100 1500
= 225
Hence the no of students ofter admission/enrolment = 1500 + 225
= 1725
Intext Questions 8.3
1. Sunita secured 76% marks, in an examination, out of total of 800. Find the
marks obtained by Sunita.
2. An employee received `15000 as bonus from the company. If the bonus is
20% of the total annual income, then find his annual income.
3. 60% of a number is 48. Find that number.
4. Reena secured some marks in an examination. In the same examination Seema
secured 20% more marks. If the maximum marks of the examination were 600.
Total marks secured by them were 720, find the marks secured by each one of
them.
8.3 Profit and Loss
Every day we make purchases from the market mostly we purchase these items
from the retailers. The retailer makes purchases from the whole seller. This amount
is called the cost price of the retailer. The retailer sells goods to the customer,
This is called selling price of that thing. This is clear if the selling price is more
than the cost price, then whether there is a profit for the retailer or loss.
Profit = Selling Price – Cost Price, Loss = Cost Price – Selling Price
Sometimes the retailer spends some amount on cartage and salary to the
employees engaged with him. These are called over head charges and the retailer
adds this into his cost price. Example. Cost Price of a TV is ` 16000 and ` 100
spent as cartage for bringing the TV then CP of TV becomes ` 16100 unless it
is made clear overhead charge are added to cost price.
Percent Profit/loss
Do remember percent profit/loss is always calculated on cost price. Let us take
an example.
Example 8.12
A shopkeeper purchased an object for ` 1400 and sold it for ` 1512. Find the
profit percent.
Sol. Cost Price = ` 1400
Selling Price = ` 1512
Profit = ` (1512–1400) = ` 112
12
Profit on ` 1400 = ` 112
12
112
Profit on ` 100 = ` 1400 ×100 = ` 8
Percent profit = `8%
Total Pr ofit 100
Percent profit = %
Cost Pr ice
Total loss 100
and Percent loss = %
Cost Pr ice
Intext Questions 8.4
1. Find the percent profit or loss in the following questions.
S.P CP Over Head Charges
(i) `550 `450 ________________
(ii) ` 1440 ` 1500 ________________
(iii) ` 300 ` 225 ` 25
(iv) ` 210 ` 190 ` 10
(v) ` 190 ` 180 ` 20
2. Ramesh purchased a table for ` 3000 and sold it for ` 2950. Find his percent
loss or profit
3. Kamini purchased a cycle for ` 1500 and sold it for ` 1800. Find his percent
profit or loss.
4. Ahmed purchased a moter cycle for ` 1200. He spent ` 1300 on it's repair and
sold it for ` 19000 Find the % profit or loss of Ahmed.
5. Ahmed purchased oranges at the rate of ` 30 per dozen and sold them at the
rate of ` 40 per dozen. Find the % loss/profit of Ahmed.
S.P, C.P, % loss / profit, out of these there if any two are given then the third can
be calculated.
Let us take some examples to explain this
Example 8.13
A horse whose cost price ` 1,35,000 was sold at a profit of 10%. What is the
SP of the horse?
Sol. Cost price of horse = `1,35000
% profit = 10
1,35,000 100 10
S.P =
100
1,35,0 00 110
= = ` 148500
100
Example 8.14
A watch was sold for ` 3290 and there was a loss of 6%. Find the cost price of
watch.
Sol. S.P = `3290, Loss = 6%
CP 100 – 6
S.P =
100
CP 94 3290 100
3290 = CP = = `3500
100 94
Intext Questions 8.5
1. Find the unknown x from the following:
S.P CP Loss% Profit%
(i) x ` 650 5 ______
1
(ii) ` 243 x ______ 12 %
2
(iii) x ` 500 ______ 5%
2
(iv) ` 250 x 16 % ______
3
(v) x ` 40 ______ 15%
2. A table was sold for ` 1920 with a loss of 4%. Find the C.P of the table.
3. A shop keeper earns 40% profit on selling an object for ` 910. Find the C.P of
that object.
4. Suresh spent ` 250 on the repair of a plough whose cost price is ` 550. He sold
1
it at a profit of 12 %. Find the S.P. of the plough.
2
Some other Examples
Example 8.15
If x is 20% more than y then find what % less of x is y?
Sol. Let the value of y be = 100
Then x will be 120 { 20% more than y}
Now when x is 120 then y = 100
100 0 250 1
When x is 100 then y = ×100 = 1000 = = 83
120 12 0 3 3
1 1 2
y from x is less % 100 – 3 % 100 83 3 % or 16 3 % less
Example 8.16:
Ali secured 434 marks in an examination with 62%. In the same examination
Ram secured 350 marks. What % marks did Ram score?
Sol. Let maximum marks = x
62
62% x = 434 100 × x = 434
434 100
or x = = 700
62
Ram secured marks = 350
350
% marks of Ram = 700 100 % = 50%
Ram secured 50% marks in the examination.
Example 8.17
A man purchased eggs at the rate of ` 48 per dozen. At what rate per egg should
he sell to receive 15% profit
Sol. Cost of 12 eggs = ` 48
48
Cost of 1 egg = = `4
12
Cost of 100 eggs = 100 × 4 = ` 400
Profit = 15%
15
Profit on 100 eggs = 100 × 4 00 = ` 60
S.P. of 100 eggs = `(400+60) = `460
Example 8.18
Ram kumar sold a radio to Dutt at a profit of 8%. Dutt spent ` 58 on it's repair
and sold it to Seema for `836. Dutt got 10% profit in this transaction. At what
price did Ram kumar sell this radio?
Sol. S.P. of Dutt = ` 836
Profit = 10%
836 100 836 100
Cost Price of Dutt = (100 10) = 110 = ` 760
This includes `58 of repair
Dutt's actual cost price = ` (760–58) = ` 702
702 100
Ram Kumar's C.P. = = ` 650
108
Cost Price of Ram Kumar = `650
Intext Questions 8.6
1. If A's value is 20% less than B's value then what percent B's value is more than
A's value?
2. After 10% reduction in the price of rice, a person can purchase 10 kg more rice
in ` 1400. Find the original price of rice and the reduced price.
3. Rama obtained 204 marks in an examination, her percent marks are 34%. If
Sophia obtained 212 marks in the same examination, find the % of marks obtained
by Sophia.
4. A man purchased oranges at the rate of `72 per dozen. At what rate per 100
she should sell them to get 20% profit.
5. Ali sold a car to Ahmed for ` 2,50,000. Ahmed spent ` 50000 on it's repair and
then sold it at a profit of 8%. Find the S.P. of the car.
8.4 Discount
To increase the sale or to sell the old articles business people given advertisement
like "prices are 30% reduced"; special sale offer at "20% off/discount" This is
sold on a special counter. The amount reduced is called "Discount". The amount
which is printed on article is called its 'market price' & the amount is reduced is
called 'Discount'. The amount paid by the customer is called the S.P. of the
article. Discount is, often, some percent of marked price. Let us take some
examples.
Example 8.19
A business man gives 15% discount on the blankets prepared by him. If the
marked price of a blanket in ` 1200, Then how much will the customer pay?
Sol. Marked price = ` 1200, Discount = 15%
15
Discount on ` 1200 = 1200 × = ` 180
100
Hence the customer will pay `1020 for the blanket
Example 8.20
The marked price of a pair of shoes is ` 1150 and the same is sold for ` 950
during sale. Find the rate of discount on the pair of shoes.
Sol. Marked price : ` 1150
Selling Price : ` 950
Total discount = ` (1150–950) = ` 200
2 00 2000
% discount = 115 0 100 % = 115 = 17.4% (Approx)
Intext Questions 8.7
1. Find the discount for the following
(i) Marked Price Discount
` 54 10
(ii) `480 6
(iii) ` 350 8
(iv) ` 150 10
(v) `160 5
2. A fan with marked price ` 2000 is sold at a discount of 15%. Find the selling
price of the fan.
3. Find the percent discount for the following
Marked Price Selling Price
(i) `65.00 ` 50.00
(ii) ` 80.00 ` 65.00
(iii) ` 120.00 ` 105.00
Let us Revise
• Percent is that fraction whose denominator is 100.
• Profit or loss percent is always caculated on the cost price.
• S.P. – CP = Profit {S.P Selling Price}
• C.P – SP = Loss { C.P Cost Price}
S.P 100 S.P 100
• C.P = 100 % Pr ofit or 100 – %loss
C.P (100 % profit) C.P (100 – % loss)
• S.P =
100
or
100
• Discount is calculated as a percent of the marked price.
Exercise
1. Write the following in percent form
7 2
(i) (ii) (iii) 0.75
10 25
(iv) 0.28 (v) 2.8
2. Write the following in the lowest form of a fraction
(i) 12% (ii) 8.2% (iii) 32%
(iv) 0.9%
3. (a) Find the value of the following
(i) 5 % of 150 (ii) 18% of 5 liter
(iii) 40% of 112kg (iv) 40% of 8 cm
(b) (i) What percent of 150 is 96?
(ii) What percent of 40 is 14?
4. Find the value of x
(i) 12% of x = 135
(ii) 80% of x = 26 liter
(iii) 4% of 8x = 36
5. Find the value of x in the following
C.P S.P % Profit % Loss Overhead Charges
(i) `400 `500 x% ____ ____
(ii) ` 400 `x 40% ____ ____
(iii) ` 150 `x ____ 20% ____
(iv) `x `400 10% ____ `50
(v) ` 900 `x ____ 10% ____
6. Sunita obtained 70% marks is an examination. If the maximum marks are 800,
find the marks obtained by Sunita.
7. Areina obtained 60 marks out of 80 in a mathematics question paper. Find
her % marks.
8. A cycle was sold at a 10% loss after purchase for ` 2400. Find the selling price
of the cycle.
9. Three articles are sold at the rate of marked price of 4 such articles. Find the %
profit.
10. Marked price of an article is ` 1600. The shopkeeper gives 20% discount.
How much will the customer pay for it?
11. The price of an article is ` 1800 after 10% discount. Find the marked price of
the article.
12. The price of an article after 35% discount is the same as that of another article
of ` 1300 after 10% discount. Find the marked price of the first article.
13. A man purchased 2 oranges for ` 10 and sold them at the rate of ` 4 per orange,
find the profit or loss%
14. A man marks 3.0%. more price on an article, also he gives 20% discount on the
new marked price. Find his profit/loss percent.
