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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.
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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