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`2000/x` 

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

∴ New cost of food for each member =` Rs 200/(x-5)` 

According of the given condition, 

`Rs 2000/(x-5)-Rs2000/x=Rs 20` 

⇒`(2000x-2000x+10000)/(x(x-5))=20` 

⇒`10000/(x^2-5x)=20` 

⇒`x^2-5x=500` 

⇒`x^2-55x-500=0` 

⇒`x^2-25x+20x-500=0` 

⇒`x(x-25)+20(x-25)=0` 

⇒`(x-25)(x+20)=0` 

⇒`x-25=0  or  x+20=0` 

⇒`x=25  or x=-20` 

∴` 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 =` Rs 2000/((25-5))=Rs2000/20=Rs100`