Amar gives Rs 9000 to some athletes of a school as scholarship every month. Had there been 20 more athletes each would have got Rs 160 less. Form a pair of linear equations for this.

This question is based on quadratic equations.

 

 

Let x = original number of athletes

9000/x - 160 = 9000/(x + 20)

(9000 - 160x)/x = 9000/(x + 20)

(9000 - 160x)(20 + x) = 9000x

180000 - 3200x + 9000x - 160x^2 - 9000x = 0

-160x^2 - 3200x + 180000 = 0

-160(x^2 + 20x - 1125) = 0

160(x + 45)(x - 25) = 0

 

Neglecting negative value, we get x = 25