Question

In a painting competition , $76$ students participated and started painting on wall.The wall has been divided into $23$ sections, Each portion will be painted by a group of either $2$ or $4$ students.Find the difference between sections painted by a group of $4$ students and by a group of $2$ students?

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

The correct option is B $7$

Let $x$ sections painted by group of $2$ students and $y$ section painted by group of $4$ students

Given that wall divided in $23$ section and total students are $76$

$\therefore x+y=23$......(1)

$\therefore 2x+4y=76$ ........(2)

Multiply equation (1) by $2$, we get

$2x+2y=46$.........(3)

Subtract equation (2) with (3), we get

$2y=30$

$\Rightarrow y=15$

Put the value $y=15$ in equation (1), we get

$x+15=23$

$\Rightarrow x=23-15$

$\Rightarrow x=8$

Then in group of $2$ students is $8$ and in group of 4 students is $15$

Then difference between sections painted by group of $4$ students and group of $2$ students $=15-8=7$