# Some students planned a picnic. The budget for food was Rs. 500. But 5 of these failed to go & thus the cost of food for each student increased by Rs. 5. How many students attended the picnic?

Let the original number of students be x.

Total budget of the food = Rs 500

Original budget of each student = If 5 students failed to go to the picnic, then

Number of student who went to the  picnic = x – 5

New budget of each student = New budget of each student  – Original budget of each student =  Rs 5      (Given) Number of students who went to the picnic = x – 5 = 25 – 5 = 20

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lete the cost of food for each student be x.

let the no. of students going to the picnic be y.

rs. 500 = x * y.......eq.1.

acc. to condition..

5 students failed to go and the price increased by rs. 5

then,

(x + 5)(y - 5)=500........eq.2.

by eq. 1 and 2 we get..

(x + 5)(y - 5)=500=x * y

(x +5)(y - 5)=x * y

xy + 5y - 5x - 25 = xy(cance xy from both sides.

5y - 5x -25 = 0

5y - 5x = 25

-5x = 25-5y

- x = (25-5y)/5

x = -(25-5y)/5

x = -5+y

put the value of x in eq. 1

500 = x*y

500 = (-5+y)*y

500 = -5y + y2

y2-5y-500=0

Y = (-b±√(b2 – 4ac))/2a

Y = (5 ± √(25 + 2000))/2

Y = (5 ± √2025)/2

Y = (5 ± 45)/2

taking positive = (5 + 45)/2

= 50/2

= 25

taking negative =( 5 - 45)/2

= -40/2

= -20

since the no. of students cannot be negative the no. of students who attempted the picnic are 25.

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