Question

some student planned a picnic .the budget for food was Rs.500. but 5 of these failed to go an then cost of food for each member is increased by Rs 5. how many students attended the picnic? write in steps plss

Answer 1

Total budget = no of students × amout brought by each student

let no. of students = x
and amount by each student = y

so ATQ
500= xy [y= 500/x]
but 5 students failed to come and 5rs were increades for everyone
so 500 = (x-5) (5y)
500 =5xy - 25y
putting value of y
500=(5x 500/x)- 25×500/x
500=2500 - 12500/x
500x = 10000
x = 20.....=>
xy=500
20y=500
y = 500/20
y = 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.

:)