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cicerone
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Problem Solving Territory: 700+ questions only.............. Updated on: 25 Sep 2008, 00:58
Originally posted by cicerone on 22 Sep 2006, 21:53.
Last edited by cicerone on 25 Sep 2008, 00:58, edited 1 time in total.
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Folks, I will be posting questions from Problem Solving section regularly in this thread.............

Here comes our first question

1. A shopkeeper increases the price of the article by X% and then decreases the resulting price by X%. As a result the price of the article is reduced by 180 $. Ater one more such cycle the price is further reduced by 153$. Find the oriiginal price of the article.



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paddyboy
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Problem Solving Territory: 700+ questions only.............. 23 Sep 2006, 00:10
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CP (1+x)(1-x) = 180
180 (1+x)(1-x) = 153 => (1-x^2) = 153/180

=> CP/180 = 180/153
=> CP = 210.60 (approx)
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cicerone
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Problem Solving Territory: 700+ questions only.............. Updated on: 25 Sep 2008, 00:57
Originally posted by cicerone on 23 Sep 2006, 02:19.
Last edited by cicerone on 25 Sep 2008, 00:57, edited 1 time in total.
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paddyboy
CP (1+x)(1-x) = 180
180 (1+x)(1-x) = 153 => (1-x^2) = 153/180

=> CP/180 = 180/153
=> CP = 210.60 (approx)
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Hey paddyboy check out again..........
u r missing something........
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Fig
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Problem Solving Territory: 700+ questions only.............. 23 Sep 2006, 02:28
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He definied x = X / 100 ;) It makes sens as x < X :)

Actually, he could set y=(1+X/100)(1-X/100) :)
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cicerone
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Problem Solving Territory: 700+ questions only.............. Updated on: 25 Sep 2008, 00:57
Originally posted by cicerone on 23 Sep 2006, 02:50.
Last edited by cicerone on 25 Sep 2008, 00:57, edited 1 time in total.
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Fig
He definied x = X / 100 ;) It makes sens as x < X :)

Actually, he could set y=(1+X/100)(1-X/100) :)
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Hey fig, that's fine.
But i said the price is decreased by 180 and not that the decreased price is 180.

So how can he write cp(1+x)(1-x) =180
CP(1+x)(1-x) is the reduced price where as 180 is the reduction in the prize.

The correct expression would be
CP(1+x)(1-x) = P-180, where P= initial price and x=X/100.
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Fig
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Problem Solving Territory: 700+ questions only.............. 23 Sep 2006, 02:55
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Absolutly :)
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paddyboy
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Problem Solving Territory: 700+ questions only.............. 23 Sep 2006, 04:45
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paddyboy
CP (1+x)(1-x) = 180
180 (1+x)(1-x) = 153 => (1-x^2) = 153/180

=> CP/180 = 180/153
=> CP = 210.60 (approx)
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DAMN! 2 days to go and I'm crapping up!!! :evil:

Okay.. here goes.

CP - CP(1-x^2) = 180
=> CP*x^2 = 180 --(1)

CP(1-x^2) - CP(1-x^2)(1-x^2) = 153
=> CP(1-x^2)x^2 = 153 --(2)

Using (2)/(1), we get
(1-x^2) = 153/180
=> x^2 = 1 - 153/180 = 27/180 = 3/20 --(3)

From (1) and (3) we get,

CP(3/20) = 180 => CP = 1200.

Howzzat? Don't tell me I'm wrong again :(
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Fig
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Problem Solving Territory: 700+ questions only.............. 23 Sep 2006, 04:55
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paddyboy
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CP (1+x)(1-x) = 180
180 (1+x)(1-x) = 153 => (1-x^2) = 153/180

=> CP/180 = 180/153
=> CP = 210.60 (approx)

Oops! 2 days to go and I'm crapping up!!! :evil:

Okay.. here goes.

CP - CP(1-x^2) = 180
=> CP*x^2 = 180 --(1)

CP(1-x^2) - CP(1-x^2)(1-x^2) = 153
=> CP(1-x^2)x^2 = 153 --(2)

Using (2)/(1), we get
(1-x^2) = 153/180
=> x^2 = 1 - 153/180 = 27/180 = 3/20 --(3)

From (1) and (3) we get,

CP(3/20) = 180 => CP = 1200.

Howzzat? Don't tell me I'm wrong again :(
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paddyboy, will u go on this monday for the GMAT? :)
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paddyboy
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Problem Solving Territory: 700+ questions only.............. 23 Sep 2006, 04:59
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Tuesday actually, but I'm not counting it... :peek
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Fig
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Problem Solving Territory: 700+ questions only.............. 23 Sep 2006, 05:04
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I c :) Best of luck for it :D U are on the right track for it :)

Next week seems to be the week for at least 3 of us ;)
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paddyboy
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Problem Solving Territory: 700+ questions only.............. 23 Sep 2006, 05:08
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Who's the third?

And dude, :beer Best of luck! I'm sure we'll maul the GMAT :2gunfire:

Or as Futuristic put it, "Spread it out on the lawn and jump on it with hob-nailed boots!" :lol:
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Fig
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Problem Solving Territory: 700+ questions only.............. 23 Sep 2006, 05:31
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I prefer to PM u it :)
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gk3.14
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Problem Solving Territory: 700+ questions only.............. 25 Sep 2006, 15:37
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cicerone
Folks, I will be posting questions from Problem Solving section regularly in this thread.............

Here comes our first question

1. A shopkeeper increases the price of the article by X% and then decreases the resulting price by X%. As a result the price of the article is reduced by 180 $. Ater one more such cycle the price is further reduced by 153$. Find the oriiginal price of the article.
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could you also give the answer choices. that way we can test the fastest way to go about this..
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cicerone
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Problem Solving Territory: 700+ questions only.............. 27 Sep 2006, 20:58
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Folks, this is again based on the basic funda of Percentages.

If a number is increased by x% and then decreased by x% there always will be a decrease.

It is given that the price (P)of the article is increased by x% and then decreased by x%. So the price will definitely decrease. Let the price decrease by y%

So clearly it is given that the price is decreased by 180 $.
Hence y%(P) = 180.............................(1)
Now the price of the artice is P-180. Since that same change is applied again on the present price this also will decrease by the same y%
Clearly it is given that the present price is decreased by 153$
Hence y%(P-180) = 153.....................(2)

From (1) and (2)
y%(180) = 27

ie y = 15.

Substituting the value of y in (1) we get
15%(P) = 180
Hence P=1200.

Now since u know the concept , u can use the options given in the exam to solve the questions like these.

Let's take 1200 as our first option
Initially the price is reduced by 180.

So the present price is 1020.

Now if 180 is the decrease on 1200, calculate the proportinate decrease on 1020.....

So i mean 1200------180
1020------??
ie (1020/1200)180 = (102/120)180 =153 which is exactly the second decrease in the given question..

Hence 1200 must be the answer........

I think i am lucid
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cicerone
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Problem Solving Territory: 700+ questions only.............. 27 Sep 2006, 21:34
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Ok folks, let's get into the next question.........

2.
Attachments

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cicerone
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Problem Solving Territory: 700+ questions only.............. 28 Sep 2006, 23:44
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Hey, what happened?

Kevin, yezz, paddyboy,......... where r u?
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ivymba
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Problem Solving Territory: 700+ questions only.............. 29 Sep 2006, 18:54
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cicerone all of them are drinking beer !!!
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Problem Solving Territory: 700+ questions only.............. 29 Sep 2006, 19:46
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CE=1, not sure on how to calculate CD :roll:
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Problem Solving Territory: 700+ questions only.............. 29 Sep 2006, 23:31
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hey, I know this problem has to be solved based on similarity of triangles. But finding it difficult to identify which triangles need to be compared.

Cicerone, great initiative. Please keep posting questions.
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cicerone
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Problem Solving Territory: 700+ questions only.............. 04 Oct 2006, 08:57
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Answer pleaseeeeeeee
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