Some students planned a picnic. The …

Let the number of students be x.
Then, cost of food for each student = Rs.{tex}\frac { 2000 } { x }{/tex}
If the number of students decreased by 5, then
new cost of food for each student = Rs.{tex}\frac { 2000 } { x - 5 }{/tex}
Now, according to question,we have
{tex}\frac { 2000 } { x - 5 } - \frac { 2000 } { x } = 20{/tex}
{tex}\Rightarrow \frac { 2000 x - 2000 x + 10000 } { x ^ { 2 } - 5 x } = 20{/tex}

{tex}\Rightarrow \frac{{10000}}{x^2 -5x} = 20{/tex}
{tex}\Rightarrow{/tex} 10000 = 20x² - 100x
{tex}\Rightarrow{/tex} 20x² - 100x - 10000 = 0
{tex}\Rightarrow{/tex} x² - 5x - 500 = 0
{tex}\Rightarrow{/tex} x² - 25x + 20x - 500 =0
{tex}\Rightarrow{/tex} x(x - 25) + x(x - 25) = 0
{tex}\Rightarrow{/tex} x - 25 = 0 or x + 20 = 0
{tex}\Rightarrow{/tex} x = 25 or x = -20

Neglecting the value of x = -20 as, number of students cannot be negative. {tex}{/tex}
{tex}\Rightarrow{/tex} x = 25
{tex}{/tex}So,the cost of food for each student is      

     {tex} \frac { 2000 } { x - 5 } = \frac { 2000 } { 25-5 } =\frac{{2000}}{20}{/tex} = 100
Hence, the number of students who attended the picnic is 25 and the cost of food for each student is Rs. 100.