#### Question

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?

#### Solution

Let *x *students planned a picnic.

Then, the share of each student `= 500/x`

According to question, 5 students fail to go picnic, then remaining students = (x - 5).

Therefore, new share of each student `500/(x-5)`

It is given that

`500/(x-5)-500/x=5`

`(500x-500x+2500)/((x-5)x)=5`

`2500/(x^2-5x)=5`

2500 = 5(x^{2} - 5x)

`2500/5=x^2-5x`

500 = x^{2} - 5x

x^{2} - 5x - 500 = 0

x^{2} + 20x - 25x - 500 = 0

x(x + 20) - 25(x + 20) = 0

(x + 20)(x - 25) = 0

x + 20 = 0

x = -20

Or

x - 25 = 0

x = 25

Because *x *cannot be negative.

Thus,* *the total numbers of students attend a picnic

= x - 5

= 25 - 5

= 20

Therefore, the total numbers of students attend a picnic be x = 20.