Question

Half of the students in a class are practising dance and three-fourths of the remaining are playing cricket. If the remaining 9 students are studying in the library, 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,
No. of students practising dance = $\frac{x}{2}$
No. of students remaining = $x-\frac{x}{2}=\frac{x}{2}$
Students playing cricket = $\left(\frac{3}{4}\right)of\left(\frac{x}{2}\right)=\frac{3x}{8}$

Remaining students = $x$ - $\frac{x}{2}$ - $\frac{3x}{8}=\frac{8x-4x-3x}{8}$

$\Rightarrow \frac{x}{8}=9$

$x=8\times 9=72$

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