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A shopkeeper increases the price of an article by X%

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A shopkeeper increases the price of an article by X% [#permalink]

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New post 28 Oct 2012, 21:45
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A shopkeeper increases the price of an article by X% and then decreases it by X%. As a result the price of the article is reduced by $180. After one more such change the price is further reduced by $153 Find the original price of the article.

A. $1200
B. $1100
C. $1400
D. $1000
E. $1500
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Re: A shopkeeper increases the price of an article by X% [#permalink]

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chris93 wrote:
A shopkeeper increases the price of an article by X% and then decreases it by X%. As a result the price of the article is reduced by $180. After one more such change the price is further reduced by $153 Find the original price of the article.

A. $1200
B. $1100
C. $1400
D. $1000
E. $1500


Let the net decrease in price after x% increase and x% decrease be a%. Also, let the initial price be $p.

Given:
After a% decrease the price of the article is reduced by $180 --> \(pa=180\);
After one more such change the price is further reduced by $153. After the first decrease the pice became \($(p-180)\), thus \((p-180)a=153\) --> \(pa-180a=153\).

Since \(pa=180\), then \(180-180a=153\) --> \(a=15%\) --> \(p*0.15=180\) --> \(p=1,200\).

Answer: A.

Hope it's clear.
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Re: A shopkeeper increases the price of an article by X% [#permalink]

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New post 16 Nov 2012, 12:48
Bunuel wrote:
chris93 wrote:
A shopkeeper increases the price of an article by X% and then decreases it by X%. As a result the price of the article is reduced by $180. After one more such change the price is further reduced by $153 Find the original price of the article.

A. $1200
B. $1100
C. $1400
D. $1000
E. $1500


Let the net decrease in price after x% increase and x% decrease be a%. Also, let the initial price be $p.

Given:
After a% decrease the price of the article is reduced by $180 --> \(pa=180\);
After one more such change the price is further reduced by $153. After the first decrease the pice became \($(p-180)\), thus \((p-180)a=153\) --> \(pa-180a=153\).

Since \(pa=180\), then \(180-180a=153\) --> \(a=15%\) --> \(p*0.15=180\) --> \(p=1,200\).

Answer: A.

Hope it's clear.


Could you explain how you got from 180 - 180a = 153 to 15% please, thank you

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Re: A shopkeeper increases the price of an article by X% [#permalink]

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New post 16 Nov 2012, 18:23
Bunuel wrote:
chris93 wrote:
A shopkeeper increases the price of an article by X% and then decreases it by X%. As a result the price of the article is reduced by $180. After one more such change the price is further reduced by $153 Find the original price of the article.

A. $1200
B. $1100
C. $1400
D. $1000
E. $1500


Let the net decrease in price after x% increase and x% decrease be a%. Also, let the initial price be $p.

Given:
After a% decrease the price of the article is reduced by $180 --> \(pa=180\);
After one more such change the price is further reduced by $153. After the first decrease the pice became \($(p-180)\), thus \((p-180)a=153\) --> \(pa-180a=153\).

Since \(pa=180\), then \(180-180a=153\) --> \(a=15%\) --> \(p*0.15=180\) --> \(p=1,200\).

Answer: A.

Hope it's clear.


Hi Bunuel,

If you increase an amount by x% and then decrease the amount by x%, is the net decrease always equal to a constant a%? You seem to assume that in your reasoning.

Thanks!
Eric

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Re: A shopkeeper increases the price of an article by X% [#permalink]

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New post 17 Nov 2012, 06:12
egiles wrote:
Bunuel wrote:
chris93 wrote:
A shopkeeper increases the price of an article by X% and then decreases it by X%. As a result the price of the article is reduced by $180. After one more such change the price is further reduced by $153 Find the original price of the article.

A. $1200
B. $1100
C. $1400
D. $1000
E. $1500


Let the net decrease in price after x% increase and x% decrease be a%. Also, let the initial price be $p.

Given:
After a% decrease the price of the article is reduced by $180 --> \(pa=180\);
After one more such change the price is further reduced by $153. After the first decrease the pice became \($(p-180)\), thus \((p-180)a=153\) --> \(pa-180a=153\).

Since \(pa=180\), then \(180-180a=153\) --> \(a=15%\) --> \(p*0.15=180\) --> \(p=1,200\).

Answer: A.

Hope it's clear.


Hi Bunuel,

If you increase an amount by x% and then decrease the amount by x%, is the net decrease always equal to a constant a%? You seem to assume that in your reasoning.

Thanks!
Eric


Yes, it does not depend on the amount. I mean that whether initial amount is $10 or $20, if you increase both by x% and then decrease both by x%, you'll get the net decrease of the same percentage:

For example if you increase both 10 and 100 by 10% and then decrease both by 10%, you'll get the net decrease of 1% for both amounts.

Hope it's clear.
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Re: A shopkeeper increases the price of an article by X% [#permalink]

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New post 17 Nov 2012, 09:34
Hi,
Is there any other method to solve this problem....if someone dont get the logic in the solution provided by Bunuel?

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Re: A shopkeeper increases the price of an article by X% [#permalink]

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New post 19 Nov 2012, 03:35
Hi Bunuel,
I have a doubt,U have equated the changed price value to 180 rather than equating the change in price.

pa is the final value after reduction in price,so to represent the change it should be p-pa=180.isnt it?

Please Correct me if i m wrong

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Re: A shopkeeper increases the price of an article by X% [#permalink]

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New post 19 Nov 2012, 03:52
kona wrote:
Hi Bunuel,
I have a doubt,U have equated the changed price value to 180 rather than equating the change in price.

pa is the final value after reduction in price,so to represent the change it should be p-pa=180.isnt it?

Please Correct me if i m wrong


We are told that after a% decrease the price of the article is reduced by $180, which means that a% of p is $180 --> pa=180.
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Re: A shopkeeper increases the price of an article by X% [#permalink]

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New post 22 Nov 2012, 04:04
hi, i was confused by the question:
A shopkeeper increases the price of an article by X% and then decreases it by X%. As a result the price of the article is reduced by $180. After one more such change the price is further reduced by $153 Find the original price of the article.

I think the question run in the following logic:
1. Price increase by x%
2. Price decrease by x %
3. After step 1 and step 2, price is reduced by $180 from the original price
4. Price increase by x%
5. Price decrease by x%
6. After step 4 and 5, price is reduced by $153 further.

Is it incorrect??

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Re: A shopkeeper increases the price of an article by X% [#permalink]

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A shopkeeper increases the price of an article by X% [#permalink]

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New post 25 Apr 2017, 08:30
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As usual Bunuel answer is best

But when i solved it , i did it this way (which is quite similar to bunuel , just more verbose)

Since p is first increased by x% and then decreased by x% , we will get
p(1 + x/100)(1 - x/100) = p-180 ---1st eq

Again the remaining amount( which is p-180) is first increased by x% and then decreased by x% , we will get
(p-180) (1 + x/100)(1 - x/100) = (p-180)-153 --- 2nd eq

Divide 1st eq by 2nd we get

p/(p-180) = (p-180)/(p-333)
(the equation is quite easy to solve once you cross multiply it)
on solving we will get p = 1200

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A shopkeeper increases the price of an article by X%   [#permalink] 25 Apr 2017, 08:30
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