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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. - ICSE Class 10 - Mathematics

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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APPEARS IN

2017-2018 (March) (with solutions)
Question 8.1 | 3.00 marks

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Solution 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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