Some students planned a picnic. The total budget for food was $R s 2000$ . But $5$ students failed to attend the picinic and thus the cost of food for each member increases by $R s 20$ . How many students attended the picinic and how much did each student pay for the food.

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Solution

Let the number of students be ‘x’

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

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