Percent change question - Original price of article reduced by 25%

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?
-32.5%
-35%
-48%
-65%
-67.5%

?

When I do it I get 32.5%, but the answer should be 48%. What am I doing wrong? Can you explain it?

Jas

x = original price

First new price = x - .25x = x(.75)

Special Sale price = First New Price - First New Price (.10) = First New Price (0.90)
Special Sale price = x(.75)(.90)
Special Sale price = x(0.675)

So you are right when you say 32.5% reduction OFF THE ORIGINAL PRICE. However that's not the question.
The question is what % do you need to raise the CURRENT sale price by to get the original price.

So take the above
Special Sale price = x(0.675) and solve for x = Original Price

Special Sale Price/0.675 = x
Special Sale Price(1.48148) = x
Breaking apart the 1.48148 so you can see how much to raise the Sale price.
Special Sale Price(1.0 + 0.48148) = x
Special Sale Price + Special Sale Price(0.48148) = x

So you need to raise the current Special Sale Price by 48.148% to get back to the original price.

Let the original price be x
Reduce it by 25%
x becomes x-0.25x = .75x
decrease the new price by 10%
0.75x - 0.75x (.10) = .75x-.075x = .675x

Original price was x ; reduced price is .675x
Assume you increase this by t% or t/100 to restore it back to x
.675x + tx/100 = x
x-tx/100 = .675x
x(1-t/100) = .675x
1-t/100 = .675
-t/100 = -.325
t/100 = .325
t = 32.5%
Increase it by 32.5% to restore it back to its original price.

No, you're right. The answer is 32.5%.

If the original price was reduce by 25%, then the price was 75% of total. If you reduce the 75% price by 10%, get 75% - 7.5% = 67.5%.

Total savings = 100% - 67.5% = 32.5%

to restore the price to 100 % of the original amount, you must increase by a factor of x:

(0.675)x = 1.0

x = [1.0/(0.675)] ≈ 1.481

the percentage increase is about 48 %

you didn't show any work !

¶

x=original price
.75(.90) x=.675x is the price after the special sale price
d(.675x)=x
d=1/.675 =1.485x
48%

100 - 32.5 = 67.5
32.5/67.5 X 100 = 48%