Answer:
If we have a given number N, and we increase it by x%, then the new number is:
N + (x%/100%)*N
While if we decrease it by x%, the new number will be:
N - (x%/100%)*N
Now, we know that:
"A number increased by a% and decreased by 80% is 400. What is the number?"
First, we can not solve the problem, because we have two unknown values, the original number and the "a%", which I guess is a typo.
So, to be general with my answer, let's assume that the actual question is:
"A number increased by 50% and decreased by 80% is 400. What is the number?"
Then, if our original number is N and we increase it by 50%, the new number will be:
N + N*(50%/100%)
N + N*0.5
N*(1 + 0.5)
N*(1.5)
Now we decrease it by 80%, and that will be equal to 400, then:
N*1.5 - N*(1.5)*(80%/100%) = 400
N*1.5 - N*1.5*0.8 = 400
N*(1.5 - 1.5*0.8) = 400
N*(0.3) = 400
N = 400/0.3 = 1,333.33...
Remember that this is a kinda general solution, so you can understand how to solve this type of problem.
