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# During a sale, the price of a pair of shoes is marked down 10% from

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Joined: 02 Sep 2009
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During a sale, the price of a pair of shoes is marked down 10% from [#permalink]

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09 Jun 2016, 03:38
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During a sale, the price of a pair of shoes is marked down 10% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?

A. 9%
B. 10%
C. 11%
D. 15%
E. 90%
[Reveal] Spoiler: OA

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Re: During a sale, the price of a pair of shoes is marked down 10% from [#permalink]

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09 Jun 2016, 04:05
Bunuel wrote:
During a sale, the price of a pair of shoes is marked down 10% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?

A. 9%
B. 10%
C. 11%
D. 15%
E. 90%

Assume the price = 100

Price during sale = 90
Price after sale = 100

Percent increase = 10/90*100 = 11% approx.

Correct Option: C
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Re: During a sale, the price of a pair of shoes is marked down 10% from [#permalink]

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09 Jun 2016, 09:55
Bunuel wrote:
During a sale, the price of a pair of shoes is marked down 10% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?

A. 9%
B. 10%
C. 11%
D. 15%
E. 90%

Let the original price = 100

Price after sale = 90, and it reverts to original price

% increase= 10/90 *100 %= 11% (approx)

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Re: During a sale, the price of a pair of shoes is marked down 10% from [#permalink]

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09 Jun 2016, 12:38
Bunuel wrote:
During a sale, the price of a pair of shoes is marked down 10% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?

A. 9%
B. 10%
C. 11%
D. 15%
E. 90%

Attachment:

Capture.PNG [ 3.49 KiB | Viewed 1917 times ]

Percent of increase = 10/90 * 100 =>11.11%

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During a sale, the price of a pair of shoes is marked down 10% from [#permalink]

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03 Aug 2017, 10:11
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Bunuel wrote:
During a sale, the price of a pair of shoes is marked down 10% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?

A. 9%
B. 10%
C. 11%
D. 15%
E. 90%

The multiplier for percent increase to get back to original (of 100 percent = 1), is the inverse of the multiplier for the original percent decrease. Then subtract 1.

Percent decrease * percent increase = 1

Ten percent decrease = $$\frac{9}{10}$$

Flip the fraction above to determine the percent by which the decreased value must increase to get to original: $$\frac{10}{9}$$ = 1.11 - 1 = .11

11%

Example:
Assume shoes cost 10

10% discount is $$\frac{9}{10}$$(10) = new price is 9

What percent increase to get back to 10?

9 * $$\frac{10}{9}$$ = 10

$$\frac{10}{9}$$ = 1.11, subtract 1 (because it already includes the 9) = 11%

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Re: During a sale, the price of a pair of shoes is marked down 10% from [#permalink]

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09 Aug 2017, 12:44
Bunuel wrote:
During a sale, the price of a pair of shoes is marked down 10% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?

A. 9%
B. 10%
C. 11%
D. 15%
E. 90%

We can let the original price = p and the percentage increase = n. Thus:

(0.9p)(1 + n/100) = p

0.9(100 + n)/100 = 1

90 + 0.9n = 100

0.9n = 10

n = 100/9 ≈ 11

Alternate Solution:

Let’s assume that the original price is 100. During the sale, the price will reduce by 10% to 90, and after the sale, the price will go up from 90 to 100. We need to determine the percent change when the price increases from 90 to 100.

percent change = 100 * (new value - old value)/(old value)

percent change = 100 * (100 - 90)/(90)

percent change = 100 * (10/90)

percent change = 100/9 ≈ 11

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Re: During a sale, the price of a pair of shoes is marked down 10% from   [#permalink] 09 Aug 2017, 12:44
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