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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Comments
Nice little problem. I have added it to my favourites. I like the solution shortcut where you divided one equation by the other. That was a shorter route than my solution.
This is a great teaser, it's too bad the truly good math teasers rarely get the rating they deserve.
Your path to a solution was really long. I did:
162 / ((162 - 147.42) / 162) = 1800
The net proportional reduction after an increase and decrease is the same as the net proportional reduction in the decrease between between the two years, which is (162 - 147.42) / 162 = .09
This means that 162 is .09 of the original price, so divide 162 by .09 (equivalent to multiplying by the reciprocal).
It took about ten seconds or so to figure out how to calculate the solution and another ten seconds or so to punch it into my calculator. (Too early in the morning to do in my head like I usually do.) I didn't even bother to wade through your solution, but it was way more involved than what the problem actually requires.
Love the teaser, not the explanation of the solution.
Your path to a solution was really long. I did:
162 / ((162 - 147.42) / 162) = 1800
The net proportional reduction after an increase and decrease is the same as the net proportional reduction in the decrease between between the two years, which is (162 - 147.42) / 162 = .09
This means that 162 is .09 of the original price, so divide 162 by .09 (equivalent to multiplying by the reciprocal).
It took about ten seconds or so to figure out how to calculate the solution and another ten seconds or so to punch it into my calculator. (Too early in the morning to do in my head like I usually do.) I didn't even bother to wade through your solution, but it was way more involved than what the problem actually requires.
Love the teaser, not the explanation of the solution.
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