Problem Solving

sanju09 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

Answer: C