Question

A 75% increase followed by a 33 1/2% decrease​

Answer 1

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
`33 (1)/(2) \%` that is 33.5%.

Let’s assume initial value be represented by variable x.

`75 \% \text { decrease means } x+75 \% \text { of } x=x+(75)/(100) x=x+0.75 x=1.75 x`

Now there is decrease of 33.5%

`\begin{array}{l}{33.5 \% \text { decrease means } 1.75 x-33.5 \% \text { of } 1.75 x=1.75 x-(33.5)/(100) * 1.75 x} \\\\ {=1.75 x-(0.335 * 1.75) x=1.75 x-0.58625 x} \\\\ {=1.16375 x}\end{array}`

`\text { So increase in percentage }=\frac{\text { final value-initial value}}{\text { intial value }}`

`=(1.16375 x-x)/(x) * 100=16.375 \%`

Hence after 75% increase followed by a
`33 (1)/(2) \%` decrease the net increased is 16.375%.