Some students planned a picnic. The total budget for food was Rs.2000 . Due to confusion 5 students failed to attend the picnic and thus the cost of food for each member increased by Rs.20. How many students attended the picnic and by how much each student pay for the food?
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2000x = (x – 5) (2000 + 20x)
2000x = 2000x + 20x2 – 10000 – 100x
0 = 20x2 – 10000 – 100x
20x2 – 10000 – 100x = 0
x2 – 500 – 5x = 0
x2 – 25x + 20x – 500 = 0
x (x – 25) + 20 (x – 25) = 0
(x + 20) (x – 25) = 0
x = –20, 25
Since, number of students is not negative, x = 25
Total number of students = 25
Number of students who attended the picnic = 25 – 5 = 20
Thus, cost for one student = Rs 2000 ÷ 20 = Rs 100
2000x = 2000x + 20x2 – 10000 – 100x
0 = 20x2 – 10000 – 100x
20x2 – 10000 – 100x = 0
x2 – 500 – 5x = 0
x2 – 25x + 20x – 500 = 0
x (x – 25) + 20 (x – 25) = 0
(x + 20) (x – 25) = 0
x = –20, 25
Since, number of students is not negative, x = 25
Total number of students = 25
Number of students who attended the picnic = 25 – 5 = 20
Thus, cost for one student = Rs 2000 ÷ 20 = Rs 100
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