Some students planned a picnic The budget for food was Rs 500 But 5 of these failed - Maths - Quadratic Equations

Question

Some students planned a picnic The budget for food was Rs 500
But 5 of these failed to go & thus the cost of food for each
student increased by Rs 5 How many students attended the
picnic?

Lalit Mehra · Accepted Answer

Let the original number of students be x.

Total budget of the food = Rs 500

Original budget of each student = $R s \frac{500}{x}$

If 5 students failed to go to the picnic, then

Number of student who went to the picnic = x – 5

New budget of each student = $R s \frac{500}{x - 5}$

New budget of each student – Original budget of each student = Rs 5 (Given)

$∴ \frac{500}{x - 5} - \frac{500}{x} = 5 \Rightarrow \frac{500 x - 500 x + 2500}{x (x - 5)} = 5 \Rightarrow \frac{2500}{x^{2} - 5 x} = 5 \Rightarrow x^{2} - 5 x = 500 \Rightarrow x^{2} - 5 x - 500 = 0 \Rightarrow x^{2} - 25 x + 20 x - 500 = 0 \Rightarrow x (x - 25) + 20 (x - 25) = 0 \Rightarrow (x - 25) (x + 20) = 0 \Rightarrow x - 25 = 0 or x + 20 = 0 \Rightarrow x = 25 or x = - 20 ∴ x = 25 (∵ x cannot be negative)$

Number of students who went to the picnic = x – 5 = 25 – 5 = 20

79

Some students planned a picnic. The budget for food was Rs. 500. But 5 of these failed to go & thus the cost of food for each student increased by Rs. 5. How many students attended the picnic?