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Some students planned a picnic. The total budget for food was Rs. 2000. But, 5 students failed to attend the picnic and thus the cost for food for each member increased by Rs. 20. How many students attended the picnic and how much did each student pay for the food?

Let x be the number of students who planned picnic

Original cost of food for each member =

5 students failed to attend the picnic, so (x – 5) students attended the picnic

New cost of food for each member =

According to the question

taking LCM

x^{2} – 5x = 500 cross multiplying

x^{2} – 5x – 500 = 0

Using the splitting middle term – the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation a = 1 b = – 5 c = – 500

= 1. – 500 = – 500

And either of their sum or difference = b

= – 5

Thus the two terms are – 25 and 20

Sum = – 25 + 20 = – 5

Product = – 25.20 = – 500

x^{2} – 5x – 500 = 0

x^{2} – 25x + 20x – 500 = 0

x(x – 25) + 20(x – 25) = 0

(x + 20) (x – 25) = 0

(x + 20) = 0 or (x – 25) = 0

x = – 20 or x = 25

x cannot be negative thus x = 25

The number of students who planned picnic = x – 5 = 25 – 5 = 20

Cost of food for each member =

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