Some students planned a picnic the budget for food was rs.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..
Answers
Let there were x students, then contribution of one student = 500x
500x
Contribution of each student when 5 of them have left = 5000x−5
5000x−5
Given, 500x−5 −500x
500x−5−500x
= 5
= 5
using options, we find x = 25 satisfies the equation.
Therefore, number of students who attended the picnic = (25 - 5) = 20.
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.
:)