Since the ratio of $ 50 notes and $ 20 notes is 3:5.
Let the number of $ 50 notes be 3x and the number of $ 20 notes be 5x respectively.
(∵ the ratio still remains the same i.e. 3x:5x=3:5).
(3x)×($ 50)+(5x)×($ 20)=$500
⇒150x+100x=500
⇒250x=500
On dividing both sides of the equation by '250', we get,
⇒250x250=500250
⇒x=2
∴ Number of $ 50 notes =3x=3×2=6
Similarly, number of $ 20 notes =5x=5×2=10