Question

9000 were divided equally among a certain no of persons had there been 15 less persons each would have got 50 more find original number of persons

Answer 1

Answer:

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. ans

 

Hope it helps