Getting percentage difference between two numbers?

Question

For example, if someone got a raise in salary and they were getting paid 80,000 and are now getting paid 85,000 how can you work out what percentage their raise was?

Answer 1

Percentage change : 100 % times the (Fractional change )

Fractional change : $\frac{85000-80000}{80000}$=$\frac{5000}{80000}$=$\dfrac{1}{16}$

Percentage change : $100\cdot\dfrac{1}{16}$% = $\dfrac{25}{4}$% = $6.25$%

Answer 2

$100*\frac{new-original}{original}$

That will get the percent :)

Answer 3

Simple Algebraic intuition : Let the percentage be $x$. Now ask $what\ \%$ of $80000$ gets added to $80000$ to get $85000$. Express it in the form of an equation.

$$\begin{align} 80000+\left(\frac{x}{100}\times80000\right)&=85000 \\ \implies\ \ \ x&=\dfrac{85000-80000}{80000}\times100 \\ &=6.25 \end{align}$$