percentage

Question

the revenue of a company increased by 30% in year one and decreased by 25% in year two. what is the overall change over the two year period

Answer 1

This is a good one!!   I hope you have an understanding of algebra and are comfortable using variables.

 

I will use R as the original or beginning revenue.

 

I will use R1 as the revenue after year one .  Thus R1=R + .30R   or    R1=1.3R

 

That being done, I'll use R2 as the revenue after year two.   Since it dropped 25% from the end of year one (or R1), it is:

 

                     R2=R1- .25 times R1 or  R2=R1-.25R1

 

 

Now........... from line three, substitute for R1.   That is,  replace R1 by 1.3R

 

 

                So,    you get that  R2=1.3R-.25(1.3R)

 

                                     or     R2=1.3R - .325R

 

                                             R2=.975R

 

This means that the year two revenue is 97.5% of the original revenue.   Thus a decrease of 2 and a half percent over the two year period.     Hope this helps. 

 

It's kind of complicated, but makes sense and this problem shows how a basic understanding of algebra can really help!

Answer 2

r₀ is the initial revenue

 

r₁ is the revenue after one year and we know that it is 30% more than the year before -> r₁=r₀*1.3 (eq1)

 

r₂ is the revenue after two years and we know that it is 25% less than the year before -> r₂=r₁*0.75 (eq2)

 

Now we substitute eq1 for r₁ in eq2 and get r₂=r₀*1.3*0.75=r₀*0.975

We see that the revenue after two years equals 97.5% of the initial revenue r₀.

 

Now, what is the overall change?