Login/Sign Up
Home » Some students planned a picnic. The total budget for food was Rs. But, 5 students failed to attend the picnic and thus the cost for food for each member increased by Rs. How many students attended the picnic and how much did each student pay for the food?
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?
CBSE | Class 10 | Exercise 10e | Maths | Quadratic Equations | RS Aggarwal
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 a picnic.

\therefore Original cost of food for each member = γ \frac{2000}{x}

Five students failed to attend the picnic. So, (x-5) students attended the picnic.

\therefore New cost of food for each member = γ \frac{2000}{(x-5)}

According of the given condition,
\Rightarrow \frac{2000 x-2000 x+10000}{x(x-5)}=20
\Rightarrow \frac{10000}{x^{2}-5 x}=20
\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
\therefore x=25
(Number of students cannot
be negative)

Number of students who attended the picnic =x-5=23-5=20
Amount paid by each student for the food =\left\{\frac{2000}{(25-5)}=\frac{2000}{20}=Rs. 100\right.

i

More Material