The owner of a flower outique follows a particular pattern for his business.during a period of inflation,he raises his price by y% and during a slowdown he decreases his existing price by y%.after a year in which there was inflation first,followed by slowdown,the cost of redrose chrysanthemum bouqet decreses by rs.162.after another yearin which thete was inflation once more followed by a slowdown,the cost of this bouquet reduces by a further rs.147.42.what was the original price of red-rose chrysanthemum bouquet?

• Let the original price of the Red Rose bouquet be Rs.'B'.
  It is given that during a period of inflation, he raises his prices by Y% and during a slowdown he decreases his existing prices by Y%.
  
  Hence after a year in which there was inflation first, followed by a slowdown, and the cost of a Red Rose bouquet decreased by Rs.162, the price of the bouquet
  = B(1+Y)(1-Y)
  = B(1-Y^2)
  (since B(1+Y) is the price during inflation and B(1-Y)(1+Y) the price during the slowdown)
  
  Therefore the decrease in price after one year
  = B - B(1-Y^2)
  = B - B + B*Y^2
  = B*Y^2 = 162 ... Equation 1
  
  Hence after another year in which there was inflation first, followed by a slowdown, and the cost of a Red Rose bouquet decreased by Rs.147.42, the price of the bouquet
  = B(1-Y^2)(1+Y)(1-Y)
  = B(1-Y^2)(1-Y^2)
  = B(1-Y^2)^2
  (since B(1-Y^2) is the price at the end of the previous year and B(1-Y^2)(1+Y)(1-Y) the price during the slowdown this year)
  
  Therefore the decrease in price this year
  = B(1-Y^2) - B(1-Y^2)^2
  = B(1-Y^2)[1 - (1-Y^2)]
  = B(1-Y^2)( Y^2) = 147.42 ... Equation 2
  
  Dividing Equation 2 by Equation 1, we get
  (1-Y^2) = 0.91 => Y^2 = 0.09
  
  Substituting the above value of Y^2 in equation 1, we get
  B*0.09 = 162
  Hence B = 162/0.09 = Rs.1800.
  
  Therefore the original price of the Red Rose bouquet is 1800 Roka.
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• ans:rs1875
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