HolaMaven wrote:

The original price of an article was reduced by 25%. During a special sale the new price was decreased by 10%. By approximately what percentage would the new price 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%

Expanding a bit on pips883's good answer, because this method is easier for me than picking numbers with percent change - a rare phenomenon.

Percentage increase and percentage decrease are inversely proportional.

To find percentage by which the changed number must increase or decrease to return to the original

1) Find the fraction for the first change

2) Flip that fraction, and

3) Calculate decimal value. That's the answer.

Here the article was reduced in price twice, by 25 percent and then 10 percent of that.

First decrease = .75 or \(\frac{3}{4}\), and second decrease, taken with the first, = .90 or \(\frac{9}{10}\)

Total decrease: \(\frac{3}{4}\) * \(\frac{9}{10}\) = \(\frac{27}{40}\)

Flip that fraction: \(\frac{40}{27}\)

\(\frac{40}{27}\) = 1.481, approximately 48%

That's the percentage by which the reduced price must [you-tube]increase[/you-tube] to return to original.

Answer C

**Or multiply the multipliers --> (.75)(.9) = .625. Change to fraction \(\frac{625}{1000}\) = \(\frac{27}{40}\). Flip and find decimal value.

Completely agree on that. Actually, my first thought when solving this question was "Come on, pick 10 and do the math". Then I realized that would be much easier if I worked with fractions. So, 99.9% times I pick numbers, but sometimes algebra may be the easiest path.

By the way, thanks for clarifying my solution. It looks much better now.