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?

Answer 1

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

∴ Original cost of food for each member =Rs${\displaystyle \frac{2000}{x}}$ 

Five students failed to attend the picnic So ${\displaystyle (x-5)}$ students attended the picnic. 

∴ New cost of food for each member =${\displaystyle Rs\frac{200}{x-5}}$ 

According of the given condition, 

${\displaystyle Rs\frac{2000}{x-5}-Rs\frac{2000}{x}=Rs20}$ 

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

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

⇒${\displaystyle x^2-5x=500}$ 

⇒${\displaystyle x^2-55x-500=0}$ 

⇒${\displaystyle x^2-25x+20x-500=0}$ 

⇒${\displaystyle x(x-25)+20(x-25)=0}$ 

⇒${\displaystyle (x-25)(x+20)=0}$ 

⇒${\displaystyle x-25=0 \text{or} x+20=0}$ 

⇒${\displaystyle x=25 \text{or}x=-20}$ 

∴${\displaystyle x=25}$                            (Number of students cannot
be negative) 

Number of students who attended the picnic ${\displaystyle =x-5=23-5=20}$ 

Amount paid by each student for the food =${\displaystyle Rs\frac{2000}{(25-5)}=Rs\frac{2000}{20}=Rs100}$