Question

In an examination $67\%$ of the students in Mathematics and $76\%$ of the students in science passed. If $19\%$ of the students failed in both the subjects and $310$ students passed then the total number of students will be

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

Answer 1

The correct option is C $500$

$\%$ of the students failed in Maths
$=100-67=33\%$
$\%$ of the students failed in Sciences
$=100-76=24\%$
and $\%$ of the students failed both subjects
$=19\%$
$\therefore \%$ of the students passed in both the subjects
$=[100-(33+24-19\left)\right]\%$
$=62\%$
$\therefore$ Total number of students
$=\frac{100\times 310}{62}=500$