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?

Answer 1

Let x students planned a picnic.

Then, the share of each student ${\displaystyle =\frac{500}{x}}$

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

Therefore, new share of each student ${\displaystyle \frac{500}{x-5}}$

It is given that

${\displaystyle \frac{500}{x-5}-\frac{500}{x}=5}$

${\displaystyle \frac{500x-500x+2500}{(x-5)x}=5}$

${\displaystyle \frac{2500}{x^2-5x}=5}$

2500 = 5(x² - 5x)

${\displaystyle \frac{2500}{5}=x^2-5x}$

500 = x² - 5x

x² - 5x - 500 = 0

x² + 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.