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.

Some students planned a picnic. The budget for food was ₹ 480. But, eight of these failed to go and thus the cost of food for each member increased by ₹ 10. How many students attended the picnic?

Answer 1

Let x students planned a picnic.

Then, the share of each student `= 480/x`

According to question, 8 students fail to go picnic, then remaining students = (x − 8).

Therefore, new share of each student `480/(x-8)`

It is given that

`480/(x-8)-480/x=10`

`(480x-480(x-8))/(x(x-8))=10`

`(480x+3840-480)/(x^2-8x)=10`

`3840/(x^2-8x)=10`

`3840/10 = x^2 - 8x`

384 = x² − 8x

x² − 8x − 384 = 0

x² + 16x − 24x − 384 = 0

x(x + 16) − 24(x + 16) = 0

(x + 16) (x − 24) = 0

x + 16 = 0

x = −16

Or

x − 24 = 0

x = 24

Because x cannot be negative.

Thus, the total numbers of students attend a picnic

= x − 8 = 24 − 8 = 16

Therefore, the total numbers of students attend a picnic be x = 16.