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Rs. 9000 Were Divided Equally Among a Certain Number of Persons. Had There Been 20 More Persons, Each Would Have Got Rs. 160 Less. Find the Original Number of Persons. - Mathematics

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Question

Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.

Solution

Let the original number of persons be x.
Then, by the given information,

`9000/x-160=900/(x+20)`

`(9000-160x)/x=9000/(x+20)`

(x + 20)(9000 - 160x) = 9000x

9000x - 160x2 + 180000 - 3200x = 9000x

160x2 - 180000 + 3200x = 0

x2 - 1125 + 20x = 0

x2 - 1125 + 20x + 100 = 100

(x + 10)2 = 1225

x + 10 = 35

x = 35 - 10

x = 25

Thus, the original number of persons is Rs 25.

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APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Q: 6 | Page no. 80
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Q: 6 | Page no. 80
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Rs. 9000 Were Divided Equally Among a Certain Number of Persons. Had There Been 20 More Persons, Each Would Have Got Rs. 160 Less. Find the Original Number of Persons. Concept: Solutions of Quadratic Equations by Factorization.
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