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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

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