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Problem Solving Territory: 700+ questions only.............. [#permalink]

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22 Sep 2006, 21:53

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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. _________________

Re: Problem Solving Territory: 700+ questions only.......... [#permalink]

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25 Sep 2006, 15:37

cicerone wrote:

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.

could you also give the answer choices. that way we can test the fastest way to go about this..

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..