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?

Explanation

Let initially, the total number of students = x
Budget for food = Rs. 500
`therefore` Share of each student = Rs. `(500)/(x)`
when 5 students failed to go, then
number of students attended the picnic = x - 5
`therefore` Share of each student now = Rs. `(500)/(x - 5)`
But, in both conditions difference in the share of each student = Rs. 5
`therefore (500)/(x - 5) - (500)/(x) = 5`
`implies 500 [(x - (x -5))/(x(x-5))] = 5`
implies `x^(2) - 5x = 500`
`implies x^(2) - 5x - 500 = 0`
`implies (x - 25) (x + 20) = 0`
`therefore " x = 25 or x = - 20"`
But number of students cannot be negative.
`therefore " "x = 25`
Hence, the number of students who attended the picnic = x - 5 = 25 - 5 = 20
Remark:
If you can solve a problem of two variables with only one variable, then no harm in it.