CBSE Class 10 Answered
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.
Asked by ayush | 24 Jul, 2013, 11:29: AM
Expert Answer
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
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
Answered by | 25 Jul, 2013, 10:24: AM
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