Let assume the no. of students be x
let the cost of each student be y
so xy = 480 ⇒ y = 480/x
so 8 students didn't arrived , each food would have cost rupees 10 more (x-8)(y+10)=480
⇒ (x-8)(480/x+10)=480
⇒ x² - 8x - 384 = 0
⇒ x² + 16x - 24x - 320 = 0
⇒ (x - 24)(x + 16) = 0
so x = - 16 or 24
so number of students can't be negative
so 24 students attended the picnic.