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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. - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### 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

Solution 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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