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A shopkeeper increases the price of an article by X% [#permalink]
 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]
29 Oct 2012, 02:15
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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]
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]
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]
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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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
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Re: A shopkeeper increases the price of an article by X% [#permalink]
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]
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]
19 Nov 2012, 03:52
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Re: A shopkeeper increases the price of an article by X% [#permalink]
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]
22 Nov 2012, 04:04
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