Question

In an examination $50\%$ of the students passed in Mathematics and $70\%$ of students passed in Science while $10\%$ students failed in both subjects. $300$ students passed in both subjects. Find the total number of students who appeared in the examination. If they took an examination in only two subjects.

Answer 1

Hint: From 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 solution:
Given that,
$50\%$ of students are passed in Mathematics, then the percentage of failed students is $100\%-50\%=50\%$
$70\%$ of students are passed in Science, then the percentage of failed students is $100\%-70\%=30\%$
$10\%$ of students are failed in both the subjects, then the percentage of total failed students is
$\begin{align}
  & {{P}_{f}}=50\%+30\%-10\% \\
 & =70\%
\end{align}$
Now the total percentage of passed students is given by
$\begin{align}
  & {{P}_{p}}=100\%-70\% \\
 & =30\%
\end{align}$
Let us assume the total number of students in the class as $x$. Then the number of passed students is
$\begin{align}
  & {{N}_{p}}=x\times \dfrac{30}{100} \\
 & =0.3x
\end{align}$
But given that the number of passed students is $300$, then
\[\begin{align}
  & 0.3x=300 \\
 &\Rightarrow x=\dfrac{300}{0.3} \\
 & =1000
\end{align}\]
So, the total number of students in the class is $1000$.

Note: Students generally do mistakes at calculating the total percent of the failed students. Remember that if you fail in one subject also it will count in failed percentage. The percentage of students who failed in mathematics and the percentage of students who failed in science has 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 mathematics and science to get the total percentage of failed students.