Question

Half the students of a class are dancing and three-fourths of the remaining are playing cricket. If the remaining 9 students are studying in the library, then find the total number of students in the class.

• A. 72
• B. 84
• C. 80
• 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 dancing $=\frac{x}{2}$

Number of students remaining $=x-\frac{x}{2}$
$=\frac{x}{2}$

Students playing cricket
$=\left(\frac{3}{4}\right)\left(\frac{x}{2}\right)$
$=\frac{3x}{8}$

Remaining students $=9$

$\Rightarrow (x-\frac{x}{2})-\frac{3x}{8}=9\Rightarrow \frac{x}{8}=9\Rightarrow x=8\times 9\Rightarrow x=72$

Hence, the total number of students in the class = 72