Question

A 55% decrease followed by a 25% increase​

Answer 1

Let's say the item starts off at $100.

A 55% decrease means 100%-55% = 45% of the value is still there. The item is now worth 0.45*100 = 45 dollars.

Now increase this by 25%. The long way to do this is to add 25% of 45 onto 45

(25% of 45) + (45) = 0.25*45+45 = 11.25+45 = 56.25

Or, we can multiply 45 by 1.25 since the multiplier 1.25 represents a 25% increase

1.25*45 = 56.25

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The item was $100, it drops to $45 after the 55% decrease, then it is $56.25 after the 25% increase.

Let's compute the percent difference

A = 100 = old value

B = 56.25 = new value

C = percent difference

C = 100*(B-A)/A

C = 100*(56.25-100)/100

C = -43.75%

The negative C value indicates a percent decrease.

So combining a 55% decrease and a 25% increase leads to an overall decrease of 43.75%

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A shortcut is to multiply 0.45 and 1.25 to get 0.5625

Then subtract this from 1 to get 1-0.5625 = 0.4375

This is another way to see we have a 43.75% decrease.