some students together collect 500 rupees …

Let the total number of students be x.
Cost of food for each member Rs. {tex}\frac{500}{x}{/tex}
If the number of students decreased by 5. Then,
New cost of food for each member Rs. {tex}\frac{500}{x - 5}{/tex}
According to question,
{tex}\frac{500}{x- 5} - \frac{500}{x} = 5{/tex}
{tex}\Rightarrow \frac{ 500x - 500(x - 5)}{x(x-5)} = 5{/tex}
{tex}\Rightarrow \frac{500x - 500x + 2500}{x^2 - 5x } = 5{/tex}
{tex}\Rightarrow \frac{2500}{ x^2 - 5x } = 5{/tex}
{tex}\Rightarrow \frac{ 2500}{ 5} = x^2 - 5x{/tex}
{tex}\Rightarrow{/tex} {tex}500=x^2-5x{/tex}
{tex}\Rightarrow{/tex} {tex}x^2-5x-500=0{/tex}
{tex}\Rightarrow{/tex}{tex}x^2-25x+20x-500=0{/tex}
{tex}\Rightarrow{/tex} x(x - 25) + 20(x - 25) = 0
{tex}\Rightarrow{/tex} (x + 20)(x - 25) = 0

{tex}\Rightarrow{/tex} x=-20,25
{tex}\Rightarrow{/tex} As number of students can't be negative. {tex}\Rightarrow{/tex} x = 25
Hence, the number of students attended the picnic = x - 5
= 25 - 5 = 20.