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# Percentage of Quantity

Percentage of quantity is the fraction of the quantity in a base of hundred. In a group or collection of different objects, we can find the number of individuals from the values of their respective percentages. In the following section, we shall see such examples and find out what formulae we will need to solve these questions.

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## Percentage of Quantity

To understand this topic, suppose you may be given a number of students in the class and based on that you need to find the boys and girls. As a result, you will be asked to solve various types of questions related to a percentage. Below are various types of questions and their solution which can usually come up in the exam and are especially relevant. After that try and solve the practice questions at the end.

### Students Based Examples

What is the Percentage Change?? Learn here.

Q. In an examination, 80 % students passed in chemistry, 70 % in physics while 15 % of the total students failed in both the subjects. If 325 students passed in both the subjects, what was the total number of students that appeared in the examination?

A. 300
B. 400
C. 500
D. 600

In this question, we are given the total number of students that have passed in both the exams. If we can the find percentage of these 325 students than we can easily find the total number of students appearing for the exams. Furthermore, it is given that there are 80 % passing in chemistry and 70 % in passing in physics. Thus, we can solve this question by going through the options one by one.

Option A is not possible because the total number of students must be > 325. For option B, 325 is 81.25% of 400 and this is also not possible because the maximum passed on the subject was 80 %. For option C, 325 is 65 % of 500 and this fits all the criteria given in the question. As 65 is less than 80 and 70 and also 325 is the number of students passed in both the subjects. So, the correct answer is option C.

Q. Two students appeared in the exam. One of the students scored 6 marks more than the other and his marks were 52 % of the total sum of the marks of both the students. What were the marks scored by the weaker student?

A. 70
B. 72
C. 76
D. 78

As there is not much information given in the question, we will suppose that the student who scored fewer marks had x marks. Thus, the student who scored more marks had x + 6 marks. Therefore their total sum is 100 and the better student had 52 % of those hundred marks. So, the equation will be something like this,

(x + 6) = (52/100) x (x + 6 + x)
=> 25(x + 6) = 13(2x + 6)
=> x = 72.

So, the weaker student scored 72 marks and the better student scored 78 marks. Thus, the correct answer is B. You can also cross check the above answer. 78 is the 52 % of 150 which is given in the question.

### Voters Based Examples

Q. 4/5th voters in Vadodara promised to vote for Suraj, while the rest assured that they will vote for Suresh. Out of the total voters who decided to vote for Suraj, 10 % did not vote on the election day. While the 20 % voters for Suresh did not vote on a penultimate day. So, what was the total number of votes if Suraj got 216 votes?

A. 300
B. 200
C. 100
D. 264

Out of the total voters, 4/5 decided to vote for Suraj. Let’s suppose the total voters were 100, so the number of voters for Suraj was 80 and out of the 80, 10 % did not go to vote. So 72 voters left with Suraj. While 20 % did not vote, so 20 % of 20 is 4 and these 4 people did not vote. So total 88 % voted on the election day.

It is given that Suraj got 216 votes which are 72 % to 88 % will be 264. So, the total number of voters was 264. So, the correct answer is option D.

Learn Percentage to Decimal or Fraction Conversion here.

## Practice Questions

Q. Sachin scored a century which included 3 fours and 8 sixes. As a result, what percent of his total score did Sachin score by running between the wickets?

A. 40
B. 45
C. 50
D. 55

Q. In the recently concluded climate conference, there were 400 women, 600 men, and 500 children present. In addition to this, 20 % of the women, 30 % of the men, and 50 % of the children were engineers. Hence, how many of the total people were not engineers?

A. 900
B. 990
C. 950
D. 930

Q. Last year the Indian football team played 50 matches and 50 % of those matches. While this year they have played some matches and seems like it was compulsory for them to win 80 % of the remaining matches to maintain its existing winning percentage. So, what is the total number of matches India team has played this year?

A. 40
B. 50
C. 35
D. Insufficient data

Q. There were 75 people in the metro compartment. 36 % of them are children and the rest are adults. If 75 % of the adults are men, then how many women are there?

A. 27
B. 12
C. 48
D. 36

Q. In a recently conducted reality show the winner was probably decided on the basis of voting done through SMS. While the choice was between Ajay and Sanjay. Since Ajay got 48 % of the votes he won it by 1560 votes. Additionally, 10 % of the SMS was not valid. Thus, find the total number of SMS received.

A. 1690
B. 3610
C. 26000
D. 13520

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kiran

Total wrong teaching and examples are wrong change the mistakes of every example, I found this
change in percentage = 4/40 x 100 = 20%.

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