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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 - Mathematics

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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 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 Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6(D) | Q: 9 | Page no. 78
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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 Concept: Quadratic Equations.
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