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# 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 - ICSE Class 10 - Mathematics

#### 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

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#### APPEARS IN

Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6D | Q: 9

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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.
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