Question

Some students planned a picnic. the budget for food was rs.500.but 50 of them failed to go and thus the cost of food for each member increased by rs.5. how many students attend the picnic

Answer 1

there were 100 members .50 of them failed to go and 50 members attended the picnic.the cost of food for each 50 members increased by rs.5

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.

:)