eli5 The percentage rule

Question

Can someone explain how/why X% of Y is equal to Y% of X? I know it’s true but I can’t figure out why. Thanks!

In: 10

Answer 1

Lets say there are two numbers

X and Y

To get X% of Y

we’ll have,

X * (Y/100)
=(X*Y)/100

let this be equation 1.

Now lets say for getting Y% of X,

we’ll do Y * (X/100)
= (Y*X)/100

this our equation 2.

You see, equation 1 and equation 2 are same.

just X and Y are swapped.

so when you say 5% of 10.

you do 5*(10/100)

but when you say 10% of 5.

you do 10*(5/100).

but both will give same answer

50/100

Answer 2

Lets say there are two numbers

X and Y

To get X% of Y

we’ll have,

X * (Y/100)
=(X*Y)/100

let this be equation 1.

Now lets say for getting Y% of X,

we’ll do Y * (X/100)
= (Y*X)/100

this our equation 2.

You see, equation 1 and equation 2 are same.

just X and Y are swapped.

so when you say 5% of 10.

you do 5*(10/100)

but when you say 10% of 5.

you do 10*(5/100).

but both will give same answer

50/100