Question

In an examination $80\%$ passed in English, $85\%$ in Maths, $75\%$ in both and $40$ students failed in both subjects. Then the number of students appeared are

• A. $300$
• B. $400$
• C. $500$
• D. $600$

Answer 1

The correct option is B $400$

$n\left(E\right)=80$

$n\left(M\right)=85$

$n(E\cap M)=75$

$n(E\cup M)=n\left(E\right)+n\left(M\right)-n(E\cap M)=80+85-75=90$

$n(E\cup M{)}^{\prime }=10$

Let n be the total number of students appeared

$\frac{10}{100}\times n=40$

$\therefore n=400$