Question

In the examination $80\% $ students passed in English and $70\% $ students passed in Maths. $10\% $ students failed in both the subjects. If 144 students passed in both subjects. Find the total number of students.
A. 220
B. 230
C. 240
D. 250

Answer 1

Hint: From the given data, we will find the percentage of failed students in Mathematics and Science. Further, we will find the total percentage of failed students in class by adding the percentage of failed students in Mathematics and Science and then subtracting the percentage of Both students. From the percentage of failed students, we will calculate the percentage of passed students in both the subjects by subtracting it from the total percentage i.e. $100\% $. Then assume the total number of students as a variable and form an equation with the given data. Now solve the equation to get the total number of students.

Complete step by step answer:
Given that,
$80\% $ students passed in English, then the percentage of failed students is,
$ \Rightarrow 100\% - 80\% = 20\% $
$70\% $ students passed in Maths, then the percentage of failed students is,
$ \Rightarrow 100\% - 70\% = 30\% $
$10\% $ students failed in both the subjects.
Then, the percentage of the total failed student is,
$ \Rightarrow {P_f} = 20\% + 30\% - 10\% $
Simplify the terms,
 $ \Rightarrow {P_f} = 40\% $
Now the total percentage of passed students is given by,
${P_p} = 100\% - {P_f}$
Substitute the value in the expression,
$ \Rightarrow {P_p} = 100\% - 40\% $
Subtract the values,
$ \Rightarrow {P_p} = 60\% $
Let us assume the total number of students in the class as $x$. Then the number of passed students is
$ \Rightarrow {N_p} = x \times \dfrac{{60}}{{100}}$
Cancel out the common factors,
$ \Rightarrow {N_p} = \dfrac{{3x}}{5}$
But given that the number of passed students is 144, then
$ \Rightarrow \dfrac{{3x}}{5} = 144$
Multiply both sides by $\dfrac{5}{3}$,
$ \Rightarrow x = 144 \times \dfrac{5}{3}$
Simplify the terms,
$\therefore x = 220$
Thus, the total number of students is 220.

Hence, option (A) is the correct answer.

Note: Students generally make mistakes at calculating the total percent of the failed students. Remember that if you fail in one subject also it will count in the failed percentage. The percentage of students who failed in Maths and the percentage of students who failed in English has been calculated by counting the people who failed in both subjects. So, we need to subtract it from the sum of the percentage of students who failed in Maths and English to get the total percentage of failed students.