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Question
Rs. 480 is divided equally among 'x' children. If the number of children were 20 more, then each would have got Rs. 12 less. Find 'x'.
Solution
Total amount = Rs. 480
Let the number of children be x.
The amount each children got = `480/x`
when the number of children were 20,
Amount of each children = `480/(x + 20)`
From the given information, we have:
`480/x - 480/(x + 20) = 12`
`(480x + 480 xx 20 - 480x)/(x(x + 20)) = 12`
`9600/(x(x + 20)) = 12`
`800/(x(x + 20)) = 1`
x2 + 20x – 800 = 0
x2 + 40x – 20x – 800 = 0
x(x + 40) – 20(x + 40) = 0
(x – 20)(x + 40) = 0
x = 20, – 40
Since, number of children cannot be negative.
So, x = 20
Number of children = 20.
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