Question

Three-fourth the students of a class are playing footbal and one-third of the remaining are playing cricket. If the remaining 12 students are studying in the library, then find the total number of students in the class.

• A. 72
• B. 80
• C. 84
• D. 96

Answer 1

The correct option is A 72

Let the total number of students be $x$

According to the question,
Number of students playing football$=\frac{3}{4}x$

Number of students remaining $=x-\frac{3x}{4}$
$=\frac{x}{4}$

Students playing cricket
$=\left(\frac{1}{3}\right)\left(\frac{x}{4}\right)$
$=\frac{x}{12}$

Remaining students $=12$

$\Rightarrow \frac{x}{4}-\frac{x}{12}=12\Rightarrow \frac{x}{6}=12\Rightarrow x=6\times 12\Rightarrow x=72$

Hence, the total number of students in the class is 72.