Question

Some students planned a picnic. The budget for the food was Rs. 480. As eight of them failed to join the party, the cost of the food for each member increased by Rs. 10. Find how many students went for the picnic.

Answer 1

Let the total no. of student be x.
Cost of food for each = ₹`(480)/x`
When 8 students failed to join, then cost of food for each = `(480)/(x - 8)`
According to question
`(480)/(x - 8) - (480)/x` = 10
`(480x - 480 (x - 8))/(x (x - 8)` = 10.
`(480(x - x + 8))/(x(x - 8)` = 10
x² - 8x - 384 = 0
x² - 24x + 16x - 384 = 0
(x - 24) (x + 16) = 0
x = 24
The no. of students went for picnic
= 24 - 8
= 16.