Question

In a class of 200, 75% were present. How many were absent?
A) 150
B) 50
C) 75
D) 125

Answer 1

Hint:
Here, we will find the number of students absent in a class. First, we will find the percentage of students absent in a class and then we will find the number of students absent in a class by using the percentage formula. Percentage is defined as the number represented as a fraction of 100.
Formula Used: Percentage is given by the formula \[P = \dfrac{x}{n} \times 100\] where \[x\] is the value for which the percentage is to be calculated and \[n\] is the total value.

Complete Step by Step Solution:
We are given that in a class of 200 students, \[75\% \] of the students were present.
Total number of students in a class, \[n = 200\]
Percentage of students present in a class \[ = 75\% \]
We know that the total percentage of students in a class is \[100\% \].
Now, we will find the percentage of the students who were absent in the class.
Percentage of the students who were absent in the class can be found by subtracting the percentage of the students present in a class from the total percentage.
Percentage of the students absent in the class \[ = \] Total percentage \[ - \] Percentage of students present in a class
Substituting the different values of percentage in the above equation, we get
\[ \Rightarrow \] Percentage of the students absent in the class \[ = 100\% - 75\% \]
\[ \Rightarrow \] Percentage of the students absent in the class, \[P = 25\% \]
Now, we will find the number of students who were absent in a class from the percentage of students who were absent in a class by using the Percentage formula.
Let \[x\] be the number of students absent in a class.
By rewriting the percentage formula \[P = \dfrac{x}{n} \times 100\], we get
\[x = \dfrac{P}{{100}} \times n\]
By substituting \[P = 25\] and \[n = 200\] in the above equation, we get
\[ \Rightarrow x = \dfrac{{25}}{{100}} \times 200\]
By dividing 200 by 100, we get
\[ \Rightarrow x = 25 \times 2\]
Multiplying the terms, we get
\[ \Rightarrow x = 50\]
Therefore, the number of students absent in a class is 50.

Thus, option (B) is the correct option.

Note:
We can also find the number of students absent in a class by finding the number of students who were present in a class from the percentage of students who were present in a class by using the Percentage formula.
Let \[x\] be the number of students present in a class.
By using the percentage formula, we get
\[ \Rightarrow x = \dfrac{P}{{100}} \times n\]
By substituting the values, we get
\[ \Rightarrow x = \dfrac{{75}}{{100}} \times 200\]
By dividing the values, we get
\[ \Rightarrow x = 75 \times 2\]
\[ \Rightarrow x = 150\]
Now, we will find the number of students who were absent in the class.
Number of the students who were absent in the class can be found by subtracting the number of students present in a class from the total number of students.
Number of students absent in the class \[ = \] Total Number of students \[ - \] Number of students present in a class
Substituting the different values of percentage in the above equation, we get
\[ \Rightarrow \] Number of students absent in the class \[ = 200 - 150\]
\[ \Rightarrow \] Number of the students absent in the class \[ = 50\]
Thus, option (B) is the correct option.