Question

In an examination $70\%$ students passed both in Mathematics and Physics $85\%$ passed in Mathematics and $80\%$ passed in Physics If $30$ students have failed in both the subjects then the total number of students who appeared in the examination is equal to :

• A. $900$
• B. $600$
• C. $150$
• D. $100$

Answer 1

The correct option is B $600$

Student passed in atleast one subject
$=n$ $(P\cup M)=n\left(P\right)+n\left(M\right)-n(P\cup M)$
$=80+85-70=95$
$\therefore$ $5\%$ student failed in both the subjects
$\Rightarrow$$5\%$ of total students $=30$
$\Rightarrow$Total students = $\frac{30\times 100}{5}=600$