At a store, they cut the price 40% for a particular item. By what percent must the item be increased if you wanted to sell it at the origina

Here's one more way.....for argument's sake let the original price be $100.

Then, the new price is just $60

So to find the percent increase to raise this back to the original price we have

[100- 60]/60 x 100%  = 40/60 x 100%  = 2/3 x 100%  = about [66 + 2/3] %

You must multiply the original price with the 40%. After that, you add the orginal price with the answer you got after multiplying the original price with 40%.

If this wasn't the answer you were looking for... I don't know what to tell you.

lets work through this one - it is a good question.    Don't worry anon, this was a very tricky question. 

Let the original price be $100.   It makes no difference what you choose for the original price but most people with find it easier if you choose an easy number rather than a letter.

alright we reduce this by 40% so the new price will be 100 - 40% of 100 = $60

so the question becomes   (where x% is the price increase)

60 + x% of 60 = $100

$$\\60+\frac{x}{100}*60=100\\\\
\frac{x}{100}*60=40\\\\
\frac{x}{100}=\frac{40}{60}\\\\
\frac{x}{100}=\frac{2}{3}\\\\
x=\frac{2}{3}\times 100\\\\
x=66\frac{2}{3}\\\\
$So the price would have to increase by $ 66\;\frac{2}{3} \;\%$$

Actually I turned this into a much harder looking question than necessary.

again let the original price by $100

40% discount brings he price down to $60

now we need to add the $40 back on.

What percent of $60 is $40 ?

   $$\frac{40}{60}\times 100=\;66\frac{2}{3}\%$$