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प्रश्न
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.
उत्तर
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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