The median of the following frequency distribution is $50$ and the total frequency is $60$. Find the missing frequencies $x$ and $y$.

Class	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$
Frequency	$5$	$x$	$20$	$y$	$2$

(A) Given total frequency $N = 60$.
Sum of frequencies: $5 + x + 20 + y + 2 = 60 \implies x + y + 27 = 60 \implies x + y = 33$ (Equation $1$).
Since the median is $50$,the median class is $40-60$. Here,$l = 40$,$h = 20$,$f = 20$,$cf = 5 + x$,and $N/2 = 30$.
Using the median formula: $\text{Median} = l + \left( \frac{\frac{N}{2} - cf}{f} \right) \times h$.
$50 = 40 + \left( \frac{30 - (5 + x)}{20} \right) \times 20$.
$50 = 40 + (25 - x)$.
$50 = 65 - x \implies x = 15$.
Substituting $x = 15$ in Equation $1$: $15 + y = 33 \implies y = 18$.
Thus,$x = 15$ and $y = 18$.