Ra 1,200 was divided equally among a certain number of children Had there been 5 children more, each would have received rupees 8 less Taking the original number of children x; find :


a) money received by each child in the first case .

b) money received by each child in the second case.

c) the original number of children

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Answers

2016-02-13T22:08:23+05:30
No. of children = x
Therefore, earlier each child got = Rs. 1200/x

New no. of children = (x+5)
Amount each child got = 1200/x - 8 = Rs. (1200-8x)/x
But, amount each child got is also Rs. 1200/(x+5)

Therefore,=> 1200/(x+5) = (1200-8x)/x
=> 1200x = (1200-8x)(x+5)
=> 1200x = 1200x+6000-8x^2-40x
=> 0 = -8x^2-40x+6000
=> 0 = x^2+5x-750 (Dividing both sides by -8)
=> 0 = x^2+30x-25x-750
=> 0 = x(x+30)-25(x+30)
=> 0 = (x-25)(x+30)
=> x = 25 or -30
discarding -ve value
=> x = 25 children

Each child originally got =(1200/25) = Rs. 48
Each child finally got = (1200/(25+5)) = Rs. 40

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