Let the no. of students planned a picnic = x
Budget for food = Rs 480
Budget for each student = 480/x
If eight student failed to join the party, the cost for each student = 480/(x - 8).

But the number of students can not be negative.
x = 24
So, the number of student who went for picnic
= x - 8 = 24 - 8 = 16