Volume of liquid $X$ in container $A = 50\,l$, Volume of liquid $Y$ in container $B = 100\,l$
$\rightarrow$ After mixing $30\,ml$ of liquid from $A$ to $B$
In Container $A$ :
- Volume of liquid $X=50l -30\,ml=49970\;ml$
In Container $B$ :
- Volume of liquid $X$ = $30\,ml$ , Volume of liquid $Y$ = $100\,l$
- $\%$ of liquid $X$ = $\frac{30}{100030}$, $\%$ of liquid $Y = \frac{100000}{100030}$
$\rightarrow$ After mixing $20\,ml$ of liquid from container $B$ to $A$:
In Container $A$ :
- Volume of $Y\,(V_{AY})$ = $20*\frac{100000}{100030}=\frac{2000000}{100030}$
In Container $B$ :
- Volume of $X\,(V_{BX})$ = $30-\left(\frac{30}{100030}*20\right) = \frac{3000300}{100030}$
So, $V_{AY} < V_{BX}$, option $(A)$ should be correct.