After 75% increase followed by a 33 1/2% decrease the net increased is 16.375%.
Solution:
Need to determine net percentage increase or decrease when a value is increased by 75% and then decreased by [tex]33 \frac{1}{2} \%[/tex] that is 33.5%.
Let’s assume initial value be represented by variable x.
[tex]75 \% \text { decrease means } x+75 \% \text { of } x=x+\frac{75}{100} x=x+0.75 x=1.75 x[/tex]
Now there is decrease of 33.5%
[tex]\begin{array}{l}{33.5 \% \text { decrease means } 1.75 x-33.5 \% \text { of } 1.75 x=1.75 x-\frac{33.5}{100} \times 1.75 x} \\\\ {=1.75 x-(0.335 \times 1.75) x=1.75 x-0.58625 x} \\\\ {=1.16375 x}\end{array}[/tex]
[tex]\text { So increase in percentage }=\frac{\text { final value-initial value}}{\text { intial value }}[/tex]
[tex]=\frac{1.16375 x-x}{x} \times 100=16.375 \%[/tex]
Hence after 75% increase followed by a [tex]33 \frac{1}{2} \%[/tex] decrease the net increased is 16.375%.
