Question

Some students planned a picnic. The budget for food was $Rs.500$. But, $5$ of them failed to go and thus the cost of food for each member increased by $Rs.5$. How many students attended the picnic ?

• A. $15$
• B. $25$
• C. $20$
• D. $30$

Answer 1

Answer: (C)

Let the total number of students be $x$.

$\Rightarrow$ Number of students attended the picnic $=x-5$

[Since, five students are not attended]

Let cost of food for each member be $y$.
$\Rightarrow xy=500$ ...(i)

After decreasing five members, cost of food for each member increased by $Rs.5$
$\Rightarrow (x-5)(y+5)=500$

$\Rightarrow xy+5x-5y-25=500$

$\Rightarrow 500+5x-5y-25=200$ [$\because xy=500$]

$\Rightarrow 5x-5y=500-500+25$

$\Rightarrow 5x-5y=25$

$\Rightarrow x-y=5$ or $y=x-5$
Puting in equation (i)
$x(x-5)=500$
$\Rightarrow x^2-5x-500=0$

$\Rightarrow x^2-25x+20x-500=0$

$\Rightarrow x(x-25)+20(x-25)=0$

$\Rightarrow (x-25)(x+20)=0$
$\Rightarrow x=25,x=-20$

Since, the number of persons is positive.

So, the total number of students $=25$
Number of students attended the picnic $=25-5=20$