ICSE Class 8 Maths Chapter 09 Percent and Percentage

Chapter 9

Percent And Percentage

Review

Test Yourself

1. \[\frac{7}{10} = \frac{7}{10} \times \ldots\ldots \% = \ldots\ldots \%\]

2. \[0.087 = 0.087 \times \ldots\ldots \% = \ldots\ldots \%\]

3. 37.5% as a vulgar fraction = \[\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\]

4. 5.6% as a decimal fraction = \[\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\]

5. 32 as the percent of 40 = \[\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\] = \[\ldots\ldots\]

6. 12.5% of 80 m = \[\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\] = \[\ldots\ldots\]

7. A number is changed from 60 to 75

Increase in number = \[\ldots\ldots\] - \[\ldots\ldots\] = \[\ldots\ldots\] and increase % = \[\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\] = \[\ldots\ldots\]

8. A number is changed from 75 to 60

Decrease in number = \[\ldots\ldots\] - \[\ldots\ldots\] = \[\ldots\ldots\] and decrease % = \[\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\] = \[\ldots\ldots\]

Teacher's Note

Percentages help us understand real-world comparisons, like calculating discounts while shopping or tracking grades in school. When a shirt costs 1000 rupees and gets a 20% discount, you save 200 rupees - a practical use of percentage calculations in daily life.

Example 1

(i) Find, 36 is what percent of 144.

(ii) 80 is 32% of a certain number, find the number.

(iii) Evaluate : 16% of 150 - 25% of 84 + 8% of 550.

Solution

(i) Direct method :

The required percent = \[\frac{36}{144} \times 100\% = 25\%\]

Alternative method :

Let x% of 144 = 36 \[\Rightarrow \frac{x}{100} \times 144 = 36 \Rightarrow x = \frac{36 \times 100}{144} = 25\]

Therefore, the required percent = 25%

(ii) Given : 32% of a certain number = 80

\[\Rightarrow \frac{32}{100} \times \text{The number} = 80 \Rightarrow \text{The required number} = 80 \times \frac{100}{32} = 250\]

Alternative method :

Let the required number be x

\[\therefore 32\% \text{ of } x = 80 \Rightarrow \frac{32}{100} \times x = 80 \text{ i.e. } x = 80 \times \frac{100}{32} = 250\]

Therefore, the required number = 250

(iii) 16% of 150 - 25% of 84 + 8% of 550

\[= \frac{16}{100} \times 150 - \frac{25}{100} \times 84 + \frac{8}{100} \times 550 = 24 - 21 + 44 = 47\]

Teacher's Note

These methods show that percentages connect to fractions and decimals, helping us solve problems about parts of wholes. In a test where you score 36 out of 144 total marks, finding the percentage tells you exactly how well you performed.

Example 2

A man spends 65% of his salary and saves 525 rupees per month. Find his monthly salary.

Solution

Since, the man spends 65% of his salary

\[\therefore\] He saves (100 - 65)% = 35% of his salary

Given : 35% of his monthly salary = 525 rupees

\[\Rightarrow \frac{35}{100} \times \text{his monthly salary} = 525\]

\[\therefore \text{His monthly salary} = 525 \times \frac{100}{35} = 1,500\]

Alternative method :

Let the man's monthly salary be 100 rupees

\[\therefore \text{He spends} = 65\% \text{ of } 100 = \frac{65}{100} \times 100 = 65\]

and, saves = 100 - 65 = 35 rupees

Applying Unitary method :

When the man saves = 35 rupees, his monthly salary = 100 rupees

\[\Rightarrow \text{When the man saves} = 1 \text{ rupee, his monthly salary} = \frac{100}{35}\]

And, when the man saves = 525 rupees, his monthly salary = \[\frac{100}{35} \times 525 = 1,500\]

Therefore, man's monthly salary = 1,500 rupees

Teacher's Note

Understanding salary percentages helps in budgeting real income. If you earn 1,500 rupees monthly and save 35%, you automatically know you spend 65% or about 975 rupees on expenses.

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