Question

In a examination, $45\%$of the candidates have passed in English, $40\%$ have passed in Hindi, while $30\%$ have passed in both the subjects. find the total number of candidates, if $90$ of them have failed in both the subjects.

• A. $100$
• B. $200$
• C. $50$
• D. None of the above

Answer 1

The correct option is B $200$

Let, $E$ be the set of candidates who passed in English and $H$ be the set of candidates who passed in Hindi.

Given: $n\left(E\right)=45\%,n\left(H\right)=40\%,n(E\cap H)=30\%$
And candidates failed in both the subjects $=90$

To find : Total number of candidates

Since, $n\left(EUH\right)=n\left(E\right)+n\left(H\right)-n(E\cap H)$
$=45\%+40\%-30\%$
$=55\%$
This means that $55\text{\%}$candidates passed in at least one of the two subjects.
Therefore,
Candidates failed $=100\text{\%}-55\text{\%}=45\text{\%}$
And candidates failed in both the subjects $=90$

Let,$x$be the total number of students,
So, $45\text{\%}ofx=90$
Or $0.45x=90$
$x=200$
Hence, Total number of candidates $=200$