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.

Answer 1

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.