A man bought a certain number of chairs for Rs.10000. He kept one for his own use and sold the rest at the rate Rs.50 more than he gave for one chair. Besides getting his own chair for nothing, he made a profit of Rs.450. How many chairs did he buy?

• 20 chairs
  
  Let the number of chairs bought=x, then
  CP of 1 chair = 10000/x
  SP of 1 chair = (10000/x)+50
  As he kept 1 chair and sold (x-1) chairs, so total SP=(x-1)*[(10000/x)+50]
  Profit = SP - CP = (x-1)*[(10000/x)+50] - 10000 = 450
  On simplifying, we get x² - 10x - 200 = 0
  => (x+10) (x-20) = 0
  So x=20
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