Use Of Percentages

We saw how percentages were helpful in comparison. We have also learnt to convert fractional numbers and decimals to percentages. Now, we shall learn how percentages can be used in real life. For this, we start with interpreting the following statements:

5% of the income is saved by Ravi. — 20% of Meera’s dresses are blue in colour.
Rekha gets 10% on every book sold by her.

What can you infer from each of these statements?

By 5% we mean parts out of 100 or we write it as 5100. It means Ravi is saving ₹ 5 out of every ₹ 100 that he earns.

In the same way, interpret the rest of the statements given above.

Converting Percentages to “How Many”

Example 6: A survey of 40 children showed that 25% liked playing football. How many children liked playing football?

Instruction

Finding percentage for football

Here, the total number of children are 40.
To find the numerical value of 25% of 40 we do: x
Solving the value is found to be
Hence, 10 children out of 40 like playing football.

1. Find:

Note : Formula: Precentage = PercentageValue100 × Total Value

(a) 50% of 164

= 50100 × 164

= × 164 =

(b) 75% of 12

= 75100 × 12

= × 12 =

(c) 1212% of 64

= First convert 1212 into decimal % .

= 12.5100 × 64

= × 64 =

2. 8% children of a class of 25 like getting wet in the rain. How many children like getting wet in the rain.

= 8% of 25 = 8100 × 25 = × 25 =

So, children like getting wet in the rain.

Example 7: Rahul bought a sweater and saved Rs. 200 when a discount of 25% was given. What was the price of the sweater before the discount?

Instruction

Original cost of sweater

Given that: 25% of original price is equal to Rs. 200
Let the original price be P.
To solve, we write the equation: x =
Solving the value of P is found to be
Evaluating
Therefore, the original price of the sweater is Rs. 800.

1. 9 is 25% of what number?

Instruction

Let's the required be P

25% of P = 9 ;

100 × P = 9

25P = × 100

P = 9x10025 = 9 × 4 =

2. 75% of what number is 15?

Let's the required be P

75% of P = 15 ;

100 × P = 15

4 × P =

3P4 = 15 ; 3P = 15 ×

P = 15×43 = 5 × 4 =

Sometimes, parts are given to us in the form of ratios and we need to convert those to percentages. Consider the following example:

Example 8 :Reena’s mother said, to make idlis, you must take two parts rice and one part urad dal. What percentage of such a mixture would be rice and what percentage would be urad dal?

Instruction

Finding percentage of urad dal

In terms of ratio we would write this as Rice : Urad dal = :
Writing the ratio in fractions, we get: Fraction of rice in mixture =
Fraction of urad dal in mixture =
Converting the respective fractions into percentages, we get: Percentage of rice = %
Then, percentage of urad dal = %
Thus, we have found the respective values

Example 9: If ₹ 250 is to be divided amongst Ravi, Raju and Roy, so that Ravi gets two parts, Raju three parts and Roy five parts. How much money will each get? What will it be in percentages?

Solution : The parts which the three boys are getting can be written in terms of ratios as 2 : 3 : 5. Total of the parts is 2 + 3 + 5 = .

Amounts received by each	Percentages of money for each
210 × ₹ 250 = ₹	Ravi gets 210 × 100 % = %
310 × ₹ 250 = ₹	Raju gets 310 × 100 % = %
510 × ₹ 250 = ₹	Roy gets 510 × 100 % = %

1. Divide 15 sweets between Manu and Sonu so that they get 20 % and 80 % of them respectively.

Instruction

Total number of sweets = 15

Manu gets 20% of 15 sweets = 20100 × 15 = 15 × 15 =

Sonu gets 80% of 15 sweets = 80100 × 15 = 45 × 15 =

So, Manu gets 3 sweets, and Sonu gets 12 sweets.

2. If angles of a triangle are in the ratio 2 : 3 : 4. Find the value of each angle.

Let the angles of the triangle be 2x, 3x, and 4x.

The sum of the angles in a triangle is always 180° = 2x + 3x + 4x = °

Simplify the equation: x = 180

Solve for x = 180°/9 = °

Now, find the value of each angle: 2x = 2 × ° = °

⇒ 3x = 3 × ° = ° , 4x = 4 × ° = °

So, the angles of the triangle are 40°, 60°, and 80°.

There are times when we need to know the increase or decrease in a certain quantity as percentage.

For example, if the population of a state increased from 5,50,000 to 6,05,000. Then the increase in population can be understood better if we say, the population increased by %.

How do we convert the increase or decrease in a quantity as a percentage of the initial amount? Consider the following example.

Example 10: A school team won 6 games this year against 4 games won last year. What is the per cent increase?

Instruction

Finding % increase

The increase in the number of wins (or amount of change) =
Percentage increase = ( / ) x 100 %
Therefore, percent of increase = %
We found the answer.

Example 11:The number of illiterate persons in a country decreased from 150 lakhs to 100 lakhs in 10 years. What is the percentage of decrease?

Solution :

Original amount = the number of illiterate persons initially = lakhs.

Amount of change = decrease in the number of illiterate persons = 150 – 100 = lakhs

Therefore, the percentage of decrease = amountofchangeoriginalamount × 100 = 50150 × 100 =

1. Find Percentage of increase or decrease:

– Price of shirt decreased from 280 to 210.

Percentage of decrease = 70280 × 100 = %

– Marks in a test increased from 20 to 30.

Percentage of increase = 1030 × 100 = %

2. My mother says, in her childhood petrol was ₹ 1 a litre. It is ₹ 52 per litre today. By what Percentage has the price gone up?

Total increase in petrol = 52 - 1 = ₹

Therefore, the percentage of price increase 5152 × 100 = %

Chapter 7: Comparing Quantities

Glossary

Use Of Percentages

Converting Percentages to “How Many”

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Chapter 7: Comparing Quantities

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Glossary

Use Of Percentages

Converting Percentages to “How Many”