 # Some students planned a picnic. The total budget for food was ₹2000. Question:

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

Solution:

Let x be the number of students who planned a picnic.

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

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

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

According to the given condition,

$₹ \frac{2000}{x-5}-₹ \frac{2000}{x}=₹ 20$

$\Rightarrow \frac{2000 x-2000 x+10000}{x(x-5)}=20$

$\Rightarrow \frac{10000}{x^{2}-5 x}=20$

$\Rightarrow x^{2}-5 x=500$

$\Rightarrow x^{2}-5 x-500=0$

$\Rightarrow x^{2}-25 x+20 x-500=0$

$\Rightarrow x(x-25)+20(x-25)=0$

$\Rightarrow(x-25)(x+20)=0$

$\Rightarrow x-25=0$ or $x+20=0$

$\Rightarrow x=25$ or $x=-20$

∴ x = 25                (Number of students cannot be negative)

Number of students who attended the picnic = − 5 = 25 − 5 = 20

Amount paid by each student for the food $=₹ \frac{2000}{(25-5)}=₹ \frac{2000}{20}=₹ 100$