Intuitively, why is X% of Y = Y% of X?

Question

I didn't spot this trick until I read this:

LPT: X percent of Y is equal to Y percent of X.

I know that multiplication is commutative; obviously, $\dfrac{X}{100}Y= X\dfrac{Y}{100}$. But this algebra doesn't betray the intuition that I feel I'm missing? How can this be intuited?

Answer 1

Say,You have $$ 5\%~~of~~1000$ $$

So,here, $$x=5~~and~~y=1000$$ So,you have $$5\$~~in~~100\$$$ $$And, 50\$~~in~~1000\$ $$

Now,let's say you have $$1000\%~~ of~~5\$$$ So,this time also $$x=5~~and~~y=1000~~~[according~to~your~strategy]$$

But now notice carefully..what is it saying?this time it is enlarging the 5$.How?

this means- $$ by~~100\$~~we~~have~~1000\$ $$ hence,$$by~~5\$~~we~~have~~50\$ $$