Question

Some students planned a picnic. The total budget for food was Rs.2000. But, 5 students failed to attend the picnic and thus the cost for food for each member increased by Rs.20. How many students attended the picnic and how much did each student pay for the food?

Answer 1

Let the no of students be x
let the cost of each student be y

so xy = 2000 ⇒ y = $\frac{2000}{x}$

so 5 students didn't arrived, each food would have cost rupees 20 more (x-5)(y+20)=2000

⇒ (x-5)($\frac{2000}{x}$+20)=2000

$\Rightarrow (x-5)\left(\frac{2000+20x}{x}\right)=2000$

⇒ 20x² - 100x - 10000 = 0

Divided both side 20 , we get

⇒ x² - 5x - 500 = 0

⇒ x² + 20x - 25x - 500= 0

⇒ (x - 25)(x + 20) = 0

so x = - 20 or 25

so the number of students can't be negative
so 25 students
but

5 students not attending the picnic

then

Number of student attending the picnic = 25 - 5 = 20

then
y= $\frac{2000}{x}$= $\frac{2000}{20}=100$
Therefore

total number of student attending the picnic = 20

and each paid 100 Rs

Hence, 20 students attended the picnic, and each paid 100 Rs for the food.