In the previous section we discussed some of the basics of percentage. In this section, we will see more details:
Solution:
The score 17 made by Student B is greater than the score 15 made by student A. But we cannot judge the performance by these marks because, the total marks for the two tests are different.
In such cases, we take percentage:
• Percentage marks scored by A = 15⁄20 This is a fraction. We know how to convert it into a percentage:
• (15⁄20 × 100) = 1500⁄20 = 75
∴ 15⁄20 = 75%
• Percentage marks scored by B = 17⁄25 This is a fraction. We know how to convert it into a percentage:
• (17⁄25 × 100) = 1700⁄25 = 68
∴ 17⁄25 = 68%
■ 75% is greater than 68%. So the performance of A is better.
Solved example 8.8
In a class of 52 students, 24 are boys. What is the percentage of boys and girls in the class?
Solution:
• Total number of students = 52
• No. of boys = 24.
• Percentage of boys:
24⁄52 × 100 ⇒ 6⁄13 × 100 ⇒ 600⁄13 = 46.15
∴ Percentage of boys = 46.15%
• No. of girls = 52 –24 =28.
Percentage of girls:
28⁄52 × 100 ⇒ 7⁄13 × 100 ⇒ 700⁄13 = 53.85
∴ Percentage of girls = 53.85%
■ So we have obtained the required answers. Let us add the two percentages: 46.15 + 53.85 =100%
We find that the sum of the two percentages is 100.
Solved example 8.9
A necklace is made of 150 beads. There are 45 yellow beads, 75 red beads and 30 green beads. Find the percentage of each colour beads
Solution:
• Total number of beads = 150
• No. of yellow beads = 45.
• Percentage of yellow beads:
45⁄150 × 100 ⇒ 3⁄10 × 100 ⇒ 300⁄10 = 30
∴ Percentage of yellow beads = 30%
• No. of red beads = 75.
• Percentage of red beads:
75⁄150 × 100 ⇒ 1⁄2 × 100 ⇒ 100⁄2 = 50
∴ Percentage of red beads = 50%
• No. of green beads = 30.
• Percentage of green beads:
30⁄150 × 100 ⇒ 1⁄5 × 100 ⇒ 100⁄5 = 20
∴ Percentage of green beads = 20%
■ We have obtained the required answers. Let us add the three percentages: 30 + 50 + 20 = 100%
We find that the sum of the three percentages is 100.
So we find that the sum of percentages in a problem is always 100. Sometimes we get problems that may require us to use this fact in a ‘reverse order’. One example is given below:
Solved example 8.10
A box contains 50 bulbs. 12 of them are defective. What is the percentage of the bulbs which are not defective?
• Total number of bulbs = 50
• No. of defective bulbs = 12
• Percentage of defective bulbs:
12⁄50 × 100 ⇒ 6⁄25 × 100 ⇒ 600⁄25 = 24
∴ Percentage of defective bulbs = 24%
Sum of the percentages of defective and non-defective bulbs will be 100
So the percentage of non-defective bulbs = 100 - 24 = 76%
Solved example 8.11
In a class 22% students come to school riding bicycle. 45%students come by bus. The rest walk to school. What percent of students walk to school?
Solution:
• Percentage of students using bicycle = 22%
• Percentage of students using bus = 45%
• Let x be the percentage of students who come walking.
• The sum of all the percentages should be 100
• So we can write:
22 +45 +x = 100 This is same as 67 +x =100
∴ x = 100 -67 =33%
So 33% of the total number of students in the class walk to school
In the next section we continue our discussion on percentage.
Comparing quantities using percentage
In a test, Student A scored 15 marks out of a total marks of 20. Another Teacher conducted a test on the same topic in another class. There, a Student B scored 17 marks out of 25. Whose performance is better?Solution:
The score 17 made by Student B is greater than the score 15 made by student A. But we cannot judge the performance by these marks because, the total marks for the two tests are different.
In such cases, we take percentage:
• Percentage marks scored by A = 15⁄20 This is a fraction. We know how to convert it into a percentage:
• (15⁄20 × 100) = 1500⁄20 = 75
∴ 15⁄20 = 75%
• Percentage marks scored by B = 17⁄25 This is a fraction. We know how to convert it into a percentage:
• (17⁄25 × 100) = 1700⁄25 = 68
∴ 17⁄25 = 68%
■ 75% is greater than 68%. So the performance of A is better.
Sum of percentages always 100
We have earlier seen in solved example 8.3 that the sum of the percentages is always 100. Let us see more such examples.Solved example 8.8
In a class of 52 students, 24 are boys. What is the percentage of boys and girls in the class?
Solution:
• Total number of students = 52
• No. of boys = 24.
• Percentage of boys:
24⁄52 × 100 ⇒ 6⁄13 × 100 ⇒ 600⁄13 = 46.15
∴ Percentage of boys = 46.15%
• No. of girls = 52 –24 =28.
Percentage of girls:
28⁄52 × 100 ⇒ 7⁄13 × 100 ⇒ 700⁄13 = 53.85
∴ Percentage of girls = 53.85%
■ So we have obtained the required answers. Let us add the two percentages: 46.15 + 53.85 =100%
We find that the sum of the two percentages is 100.
Solved example 8.9
A necklace is made of 150 beads. There are 45 yellow beads, 75 red beads and 30 green beads. Find the percentage of each colour beads
Solution:
• Total number of beads = 150
• No. of yellow beads = 45.
• Percentage of yellow beads:
45⁄150 × 100 ⇒ 3⁄10 × 100 ⇒ 300⁄10 = 30
∴ Percentage of yellow beads = 30%
• No. of red beads = 75.
• Percentage of red beads:
75⁄150 × 100 ⇒ 1⁄2 × 100 ⇒ 100⁄2 = 50
∴ Percentage of red beads = 50%
• No. of green beads = 30.
• Percentage of green beads:
30⁄150 × 100 ⇒ 1⁄5 × 100 ⇒ 100⁄5 = 20
∴ Percentage of green beads = 20%
■ We have obtained the required answers. Let us add the three percentages: 30 + 50 + 20 = 100%
We find that the sum of the three percentages is 100.
So we find that the sum of percentages in a problem is always 100. Sometimes we get problems that may require us to use this fact in a ‘reverse order’. One example is given below:
Solved example 8.10
A box contains 50 bulbs. 12 of them are defective. What is the percentage of the bulbs which are not defective?
• Total number of bulbs = 50
• No. of defective bulbs = 12
• Percentage of defective bulbs:
12⁄50 × 100 ⇒ 6⁄25 × 100 ⇒ 600⁄25 = 24
∴ Percentage of defective bulbs = 24%
Sum of the percentages of defective and non-defective bulbs will be 100
So the percentage of non-defective bulbs = 100 - 24 = 76%
Solved example 8.11
In a class 22% students come to school riding bicycle. 45%students come by bus. The rest walk to school. What percent of students walk to school?
Solution:
• Percentage of students using bicycle = 22%
• Percentage of students using bus = 45%
• Let x be the percentage of students who come walking.
• The sum of all the percentages should be 100
• So we can write:
22 +45 +x = 100 This is same as 67 +x =100
∴ x = 100 -67 =33%
So 33% of the total number of students in the class walk to school
In the next section we continue our discussion on percentage.
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