Rs.9000 were divided equally among a certain no.of persons.had there been 20 more persons,each would have got rs.160 less.find the original no.of persons.
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Answer is 25
Let the original no. of persons be x, then
9000 divided equally between x persons, each one get ------> 9000/x
9000 divided equally between (x + 20) persons, each one get------> 9000/(x + 20)
According to the que,
9000/(x + 20) = 9000/x - 160
=> 9000x = (x+20)(9000 - 160x)
=> 9000x = 9000x - 160x^2 + 180000 - 3200x
=> 160x^2 + 3200x - 180000 = 0
=> x^2 + 20x - 1125 = 0
=> x^2 + 45x - 25x - 1125 = 0
=> x(x + 45) - 25(x + 45) = 0
=> (x + 45)(x - 25) = 0
Either (x + 45) = 0 or ( x - 25) = 0
(x + 45) = 0 => x = - 45 (not possible)
Therefore, (x - 25) = 0 => x = 25.
Let the original no. of persons be x, then
9000 divided equally between x persons, each one get ------> 9000/x
9000 divided equally between (x + 20) persons, each one get------> 9000/(x + 20)
According to the que,
9000/(x + 20) = 9000/x - 160
=> 9000x = (x+20)(9000 - 160x)
=> 9000x = 9000x - 160x^2 + 180000 - 3200x
=> 160x^2 + 3200x - 180000 = 0
=> x^2 + 20x - 1125 = 0
=> x^2 + 45x - 25x - 1125 = 0
=> x(x + 45) - 25(x + 45) = 0
=> (x + 45)(x - 25) = 0
Either (x + 45) = 0 or ( x - 25) = 0
(x + 45) = 0 => x = - 45 (not possible)
Therefore, (x - 25) = 0 => x = 25.
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