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Rs. 480 is Divided Equally Among ‘X’ Children. If the Numbers of Children Were 20 More Then Each Would Have Got Rs. 12 Less. Find ‘X’. - Mathematics

Rs. 480 is divided equally among ‘x’ children. If the numbers of children were 20 more then each would have got Rs. 12 less. Find ‘x’.

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Solution

The number of children = x.

The share of each child = Rs `480/x`

If number of children are x + 20, then share of each child = Rs `480/(x + 20)`

According to the given information,

`480/x - 480/(x + 20) = 12`

`=> 480(1/x - 1/(x + 20)) = 12`

`=> 480(20/(x(x + 20))) = 12`

`=> (480 xx 20)/12 = x(x + 20)`

`=> x^2 + 20x - 800 = 0`

`=> x^2 - 20x + 40x - 800 = 0`

`=> (x - 20)(x + 40) = 0`

`=> x = 20 or x = -40`

But, the number of children cannot be negative.

Therefore, x = 20

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