Question

some students planned a picnic. the total budget for food was rupees 2000 but 5 students failed to attend the picnic and thus the cost of food for each member increased by rupees 20. how many students attended the picnic and how much did each had to pay for the food?

Answer 1

Let the number of students who planned a picnic be 'x'.

Given, total budget = 2000.

Then, the budget of each student = (2000)/(x).

(i)

Given that 5 students failed to attend the picnic.

Then the number of students who went to the picnic = x - 5.

So, the new budget = (2000)/(x - 5).

(ii)

Given that cost of food for each member increased by 20.

= > (2000/x - 5) - (2000/x) = 20

= > 2000(x - x + 5)  = 20x(x - 5)

= > 2000(5) = 20x(x - 5)

= > 500 = x(x - 5)

= > 500 = x^2 - 5x

= > x^2 - 5x - 500 = 0

= > x^2 - 25x + 20x - 500 = 0

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

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

= > x = 25,-20 {x cannot be negative}

= > x = 25.

So, the number of students who attended the picnic :

= > x - 5

= > 25 - 5

= > 20.

So, the budget of each student :

= > (2000)/(x - 5)

= > (2000)/(25 - 5)

= > (2000)/20

= > 100.

Therefore, 20 students attended the picnic and paid 100 rupees each for food.

Hope this helps!