Given:
12% decrease followed by a 18% increase.
To find:
The single percentage change is equivalent to the given set of percentages.
Solution:
Let the initial value be 100.
After 12% decrease, the value is:
[tex]v_1=100-\dfrac{12}{100}\times 100[/tex]
[tex]v_1=100-12[/tex]
[tex]v_1=88[/tex]
After 18% increase, the value is:
[tex]v_2=88+\dfrac{18}{100}\times 88[/tex]
[tex]v_2=88+15.84[/tex]
[tex]v_2=103.84[/tex]
The initial value is 100 and the new value in 103.84. So, it represents increase in the value. So, increase percentage is
[tex]Increase\%=\dfrac{\text{New -Initial}}{\text{Initial}}\times 100[/tex]
[tex]Increase\%=\dfrac{103.84-100}{100}\times 100[/tex]
[tex]Increase\%=3.84[/tex]
Therefore, the value increased by 3.84%.
