Question

some students planned a picnic.The budget for food was 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 no. Of students be x
Let the cost of each student be y.
X*y=500
(X-5)(y+5)=500
(x-5)(500/x+5)=500
(X-5)(500+5x/x)=500
500x+5x²/x-2500+25x/x=500
525x+5x²-2500=500x
X²+5x-500=0
(x-20),(x+25)=0
X=20or-25

Answer 2

Answer:

Step-by-step explanation:

I have explained the answer below-----------

Budget for food = ₹  500 & 5 students failed to attend the picnic.

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

Budget of each student = 500/x

Students who attended the picnic = (x - 5)

New Budget of each student = 500/(x - 5)

A.T.Q

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

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

[(500 x - 500 (x - 5)] / (x)(x - 5) = 5

500(x - x + 5) / x² - 5x  = 5

500(5) / x² - 5x = 5

2500 / x² - 5x = 5

5(x² - 5x) = 2500

x² - 5x = 2500/5

x² - 5x = 500

x² - 5x - 500 = 0

x² - 25x + 20x - 500 = 0

[By middle term splitting method]

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

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

(x - 25) = 0  or (x + 20) = 0

x = 25  or x = - 20

Since, number of students can't be negative, so x ≠ - 20.  

Therefore, x = 25

Students who attended the picnic = (x - 5) = 25 - 5 = 20  

Hence, Students who attended the picnic = 20.

:)