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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.
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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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