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Sagot :
Given:
18% increase followed by a 13% decrease.
To find:
The single percentage equivalent to a 18% increase followed by a 13% decrease.
Solution:
Let a number be 100.
If it is increased by 18% then the number becomes
[tex]Number=100+\dfrac{18}{100}\times 100[/tex]
[tex]=100+18[/tex]
[tex]=118[/tex]
Then, it is decreased by 13%.
[tex]Number=118-\dfrac{13}{100}\times 118[/tex]
[tex]=118-15.34[/tex]
[tex]=102.66[/tex]
New number is 102.66.
Now, the percentage change is
[tex]\%\text{ Change}=\dfrac{\text{New number - Initial number}}{\text{Initial number}}\times 100[/tex]
[tex]\%\text{ Change}=\dfrac{102.66-100}{100}\times 100[/tex]
[tex]\%\text{ Change}=\dfrac{2.66}{100}\times 100[/tex]
[tex]\%\text{ Change}=2.66\%[/tex]
Therefore, the Single percentage change is 2.66%.
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