Answer:
The original [tex]A[/tex] would be greater than the new value by [tex]0.25\, A[/tex].
Step-by-step explanation:
Refer to the diagram attached.
[tex]50\%[/tex] of [tex]A[/tex] is equivalent to [tex]0.5\, A[/tex].
Reducing [tex]A[/tex] by [tex]50\%[/tex] is the same as subtracting [tex]0.5\, A[/tex] from [tex]A\![/tex]. The "result" would be [tex]A - 0.5\, A = 0.5\, A[/tex].
Since the "result" is [tex]0.5\, A[/tex], [tex]50\%[/tex] of the "result" would be [tex]50\% \times 0.5\, A = 0.5\times 0.5\, A = 0.25\, A[/tex].
Adding [tex]50\%[/tex] of the "result" to the result itself would be the same as adding [tex]0.25\, A[/tex] to [tex]0.5\, A[/tex], which gives the new value [tex]0.75\, A[/tex].
Thus, the original [tex]A[/tex] would be greater than the new value by [tex]A - 0.75\, A = 0.25\, A[/tex].
