What is 5% of 40? What is 40% of 5? What is 25% of 12? What is 12% of 25? What is 15% of 60? What is 60% of 15? Class 8

What is 5% of 40? What is 40% of 5? What is 25% of 12? What is 12% of 25? What is 15% of 60? What is 60% of 15? Class 8

Question 1.

What is 5% of 40? What is 40% of 5? What is 25% of 12? What is 12% of 25? What is 15% of 60? What is 60% of 15? What do you notice?

Can you make a general statement and justify it using algebra, comparing x% of y and y% of x? Class 8

Solution:

5% of 40 = 2; 40% of 5 = 2;

25% of 12 = [latex]\frac{25}{100}[/latex] × 12 = 3,

12% of 25 = [latex]\frac{12}{100}[/latex] × 25 = 3,

15% of 60 = [latex]\frac{15}{100}[/latex] × 60 = 9,

60% of 15 = [latex]\frac{60}{100}[/latex] × 15 = 9.

Yes, x% of y is the same as y% of x.

Both equal to [latex]\frac{x}{100}[/latex] × y = [latex]\frac{xy}{100}[/latex]

Question 2.

A school is organising an excursion for its students. 40% of them are Grade 8 students and the rest are Grade 9 students. Among these Grade 8 students, 60% are girls. [Hint : Drawing a rough diagram can help]. Class 8

(i) What percentage of the students going to the excursion are Grade 8 girls?

(ii) If the total number of students going to the excursion is 160, how many of them are Grade 8 girls?

Solution:

(i) Let the number of students = 100

Students of grade 8 = 40% = 40

So, girls of grade 8 = 60% of 40

= [latex]\frac{60}{100}[/latex] × 40 = 24

Thus, required percentage of girls = 24%.

(ii) Total number of students = 160

So, grade 8 students = 40% of 160

Hence, grade 8 girls going for excursion

= [latex]\frac{60}{100}[/latex] × 64

= [latex]\frac{384}{10}[/latex] = 38.4