#### 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 bv 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`

`x^2 + 25x - 12500 = 0`

(x + 125)(x - 100) = 0

x = -125, 100

Since the number of student cannot be negative so x = 100

Hence the number of students is 100

Is there an error in this question or solution?

Solution 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 Concept: Quadratic Equations.