Question

A group of students equal in number to the square root of half the whole class is selected for a project. Two more students were selected as captain and vice captain. Rest of the class which form $\frac{8}{9}$ th of class were given leave. Find the total number of students in the class?

• A. 64
• B. 72
• C. 80
• D. 81

Answer 1

The correct option is B

72

Method 1: Conventional Method

The traditional way to solve this question is by using equations

Let the number of students in the class=x

Then, if "y” is the number of students who are selected for the project, then $y=\sqrt{\frac{x}{2}}$

also, given that $x-\sqrt{\frac{x}{2}}-2=\frac{8}{9}x$

Replace x by $a^2$

Then the equation changes to $a^2-\frac{a}{\sqrt{2}}-2=\frac{8}{9}{a}^2$

Solving, we get x=72