Page 170 - Math_Genius_V1.0_C8_Flipbook

E:\Working\Focus_Learning\Math_Genius-8\Open_Files\09_Chapter_7\Chapter_7
\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

1. Consider the situation given in ‘Get Ready’ and answer the following:
(a) What is the ratio of extra weight to the total weight?

(b) What per cent is the extra weight compared to the recommended weight of the pack?
(c) Do you think the company will make a 20% profit by reducing the weight from 100 g to 80 g?
Give a reason to support your answer.
2. Which deal is a better choice – a 50 g toothpaste for `90 or a 125 g toothpaste for `180?

A Review of Percentage and Its Application

We know that a ‘ratio’ is used to compare two quantities of the same kind by using division. The
symbol ‘:’ is used to denote a ratio and read as ‘is to’. If a and b are two quantities, then the ratio of
a
a to b is expressed as a : b or and read as ‘a is to b’.
b
8
For example, the ratio of 240 mL to 150 mL can be written as 240 : 150 or 8 : 5 or .
5
‘Percentage’ is another term used to compare two quantities. Per cent derived from Latin word
‘per centum’ means ‘per hundred’ or ‘hundredths’. Percentages are numerators of fractions with
denominators 100. For example, “6 per cent” is written as 6%, which means 6 out of 100. Therefore,
6
6% = 6 hundredths = .
100
In a class of 40 students, there are 16 girls. Let us find what per cent of students are girls and boys
as follows:

Girls: 16 out of 40 students are girls. Boys: (40 – 16) out of 40 students are boys.
16 24
That means, of the students are girls. That means, of the students are boys.
40 40
16 2 24 3
Also, we can say = Also, we can say =
40 5 40 5
×
×
220 40 320 60
⇒ = = 40% ⇒ = = 60%
520 100 520 100
×
×
So, 40% of the students are girls. So, 60% of the students are boys.
Percentage of a Number/Quantity
P
To find the percentage (P%) of a number or quantity (Q), we use the formula P% of Q = × Q.
100
1
Example 1: Find (a) 30% of 500 apples (b) 6 % of `160
4
30 1 25
Solution: (a) 30% of 500 apples = × 500 = 150 apples (b) 6 % of `160 = × 160 = `10
100 4 4 × 100
Example 2: A football team won 12 matches out of total number of matches they played. If their
win percentage was 60, then how many matches did they play in all?

Solution: Let the total number of matches played = Q. Here, 60% of Q = 12 matches.
60 12 × 100
⇒ × Q = 12 ⇒ Q = = 20
100 60
Thus, the team played 20 matches in all.

Mathematics-8 168