Question

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

• A. 96
• B. 84
• C. 80
• D. 72

Answer 1

The correct option is D 72

Let the total number of students be $\text{x}$.

According to the question,
Number of students dancing $=\frac{\text{x}}{2}$

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

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 is 72.