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Rs. 7500 Were Divided Equally Among a Certain Number of Children. Had There Been 20 Less Children, Each Would Have Received Rs. 100 More. Find the Original Number of Children. - Mathematics

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Question

Rs. 7500 were divided equally among a certain number of children. Had there been 20 less children, each would have received Rs. 100 more. Find the original number of children.

Solution

Let the original number of person be x, then 7500 divided equally between x person,

each one gets = `7500/x`

7500 divided equally between x - 20 children

each one gets `75 = 7500/(x-20)`

According to the question

`7500/(x-20) = 7500/x + 100/1`

`7500/(x - 20) = (7500 + 100x)/x`

7500x = (x-20)(7500+100x)

75x = (x - 20)(75 + x)

75x = 75x + x2 - 1500 - 20x

x2 - 20x - 1500 = 0

`x = (20 +- sqrt(400-4(-1500)))/2`

`x = (20 +- sqrt(400 + 6000))/2`

`x = (20+- 80)/2`

`x = (20+80)/2  or x= (20-80)/2`

x = 50  or x = -30 (not possible)

∴ original number of children = 50

  Is there an error in this question or solution?
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Rs. 7500 Were Divided Equally Among a Certain Number of Children. Had There Been 20 Less Children, Each Would Have Received Rs. 100 More. Find the Original Number of Children. Concept: Quadratic Equations.
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