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?

Dheeraj Kumar · Accepted Answer · 2014-12-16T15:15:23.283

6

Percentage change : 100 % times the (Fractional change )

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

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

edited Dec 16 '14 at 15:15

answered Dec 16 '14 at 11:18

Dheeraj Kumar

2,091

I realize on the first line you have to do original / difference to get the fraction, but I don't quite understand the formula on the second line. What is the dot after the 100 for? – Brett Dec 16 '14 at 11:32
"$\cdot$" stands for multiplication or "times" it is 100 times $\frac{1}{16}$ – Dheeraj Kumar Dec 16 '14 at 11:33
1

and also the fractional change is difference or (change) / original – Dheeraj Kumar Dec 16 '14 at 11:35
I think you mean 100% times fractional change? – BCLC Dec 16 '14 at 12:23
Ok, so basically it's difference / original * 100 ? – Brett Dec 16 '14 at 12:28
yes!${}{}{}{}{}$ – Dheeraj Kumar Dec 16 '14 at 12:29
Please use dfrac instead of frac when there are a lot of terms in inline formatting. It looks more neat. :) – Dec 16 '14 at 15:03
OK!${}{}{}{}{}{}{}$ – Dheeraj Kumar Dec 16 '14 at 15:05
That is a raise of $5000 per $80000. Percent means per hundred, so to convert that to a percent, we just solve x/100 = 5000/80000 for x. – Paul Dec 16 '14 at 15:53
x = 100*5000/80000 = 500000/80000 = 50/8 = 6.25 – Paul Dec 16 '14 at 15:55

score 3 · Answer 2 · answered Dec 16 '14 at 11:24

3

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

That will get the percent :)

answered Dec 16 '14 at 11:24

Kurtbusch

632

score 2 · Answer 3 · 2014-12-20T03:21:52.690

2

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.

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

edited Dec 20 '14 at 03:21

answered Dec 16 '14 at 15:10

Getting percentage difference between two numbers?

3 Answers3