Question

In an examination, 80% of the students passed in English, 85% in Mathematics and 75% in both English and Mathematics. If 40 students failed in both the subjects, find the total number of students.

• A. 350
• B. 400
• C. 450
• D. 500

Answer 1

The correct option is B 400

Let the total number of student is x
Number of student passed in both subject is
$n(A\cup B)=n\left(A\right)+n\left(B\right)-(A\cap B)$
Here, n(A)=80% of x
n(B)=85% of x
n(c)=75% of x
$\therefore n(A\cup B)=\frac{80}{100}x+\frac{85}{100}x-\frac{75}{100}x$
$\Rightarrow \frac{90x}{100}\Rightarrow \frac{9x}{10}$
Failed in both subjects
$\Rightarrow x-\frac{9x}{10}\Rightarrow \frac{x}{10}$
$\therefore \frac{x}{10}=40$
$\Rightarrow x=400$