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# The original price of an article was reduced by 25 percent.

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Manager
Joined: 03 Feb 2007
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The original price of an article was reduced by 25 percent. [#permalink]  29 Mar 2007, 10:18
The original price of an article was reduced by 25 percent. During a special sale the new price was decreased by 10 percent. By approximately what percent would the price now have to be increased in order to restore the price of the article to its original amount?

A) 32.5%
B) 35%
C) 48%
D) 65%
E) 67.5%

Is it 32.5 or 48? I figured it was 48, but PR says its 32.5
Intern
Joined: 11 Feb 2007
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let the original price be x.
reduced by 25%, it becomes, 0.75x.
reduced by another 10%, it becomes, 0.675x.

that is 67.5% of the original or a decrease in 32.5%. the price would have to be increased by 32.5% in order to get back to the original.
Manager
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let the original price be x.
reduced by 25%, it becomes, 0.75x.
reduced by another 10%, it becomes, 0.675x.

that is 67.5% of the original or a decrease in 32.5%. the price would have to be increased by 32.5% in order to get back to the original.

aren't you taking the percentage increase of the 67.5? Thus 32.5 of 67.5 is 48? When do you know to do that?
Intern
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the question asks for 'by what percent should the price be increased'. it does not ask for 'increase in percent of the price'.

think of the % as units.
Manager
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what is OA?
Manager
Joined: 28 Feb 2007
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IHATEMELGIBSON1 wrote:
The original price of an article was reduced by 25 percent. During a special sale the new price was decreased by 10 percent. By approximately what percent would the price now have to be increased in order to restore the price of the article to its original amount?

A) 32.5%
B) 35%
C) 48%
D) 65%
E) 67.5%

Is it 32.5 or 48? I figured it was 48, but PR says its 32.5

Let original price be P
Current price = 9/10 x 3/4 x P = 27/40 P

Percent increase to come to original = [P - 27/40P]/27/40P x 100
which comes to 48%

I think if this is not the answer then I am misunderstanding the question
Manager
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Po = $100 (ASSUMPTION) P1 (after 1st discount) = 75% x$100 = $75 P2 (after 2nd discount) = 90% x$75 = $67.5 P2-Po =$32.5

The percentage increase from P2 to Po (remember that our reference is still P2) is: % = (P2-Po)/Po = 32.5/67.5 = 48%

Manager
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Agree, I would also say the answer is 48% as the question asks by how much the price has to be increased. The price (currently 67.5% reduced) has to be increased by 48% to get to the original level.

Manager
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it will be 48%:-D. if oa says 32.5 % then either OA is wrong or there is some typo error in question
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