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Question
Rs. 250 is divided equally among a certain number of children. If there were 25 children more, each would have received 50 paise less. Find the number of children.
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Solution
Let the number of children be x.
It is given that Rs. 250 is divided amongst x students.
So, money received by each child = Rs. `250/"x"`
if there were 25 children more, then
Money received by each child = Rs. `250/(x + 25)`
From the given information,
`250/x - 250/(x + 25) = 50/100`
`(250x + 6250 - 250x)/(x(x + 25)) = 1/2`
`6250/(x^2 + 25x) = 1/2`
x2 + 25x – 12500 = 0
(x + 125)(x – 100) = 0
x = –125, 100
Since, the number of students cannot be negative.
So, x = 100.
Hence, the number of students is 100.
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