Question

Some students planned to go on a picnic and the total budget for food was ₹ 500 but in this 5 students were unable to go. As a result, the cost of food for each student increases to 10, then the total number of students is known.

Answer 1

let total no. of students be = x

let cost of food for each student = x rs.

A.T.Q,

xy=500. -(1)

(x-5)(y+10)=500

(x-5)(500/x +10)=500

(x-5)(500+10x/x)=500

(x-5)(500+10x)=500x

500x - 2500 + 10x^2 - 50x = 500x

10x^2 - 50x - 2500 =0

10(x^2 - 5x - 250)=0

x^2 - 5x - 250 =0

solving the equation y will get the answer.. Hope it helps

Answer 2

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By direction options,  

500/25 = 20, 500/20 = 25

By mathematical method, the main steps are :

xy=500          ...(i)

and (x−5)(y+5)=500

⇒x−y=5 or y=x−5

Puting in equation (i)

x(x−5)=500

⇒x^2−5x−500=0

⇒x=25 and attended =x−5=20