### Brain Teasers

# Boutique Bouquets ...

Fun: (2.21)
Difficulty: (2.74)
Puzzle ID: #19273

Submitted By: lesternoronha1 Corrected By: shenqiang

Submitted By: lesternoronha1 Corrected By: shenqiang

The owner of a Romankachi flower boutique follows a particular pattern for his business. During a period of inflation, he raises his prices by Y% and during a slowdown he decreases his existing prices by Y%. After a year in which there was inflation first, followed by a slowdown, the cost of a Red Rose bouquet decreases by 162 Roka (Roka being the native Romankachi currency). After another year in which there was inflation once more followed by a slowdown, the cost of this bouquet reduces by a further 147.42 Roka. What was the original price of the Red Rose bouquet ?

### Answer

The original price of the Red Rose bouquet is 1800 Roka.Let the original price of the Red Rose bouquet be 'B' Roka.

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 162 Roka, 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 147.42 Roka, 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 = 1800 Roka.

Therefore the original price of the Red Rose bouquet is 1800 Roka.

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