Solution

In container $A$, alcohol : water $=5:3$.

So, alcohol fraction in $A$ is:

$\frac{5}{8}$

In container $B$, alcohol : water $=1:3$.

So, alcohol fraction in $B$ is:

$\frac{1}{4}$

Required total mixture is $2.1$ litres, and alcohol and water are equal.

So, required alcohol quantity is:

$\frac{2.1}{2}=1.05$

Let $x$ litres be drawn from container $A$.

Then liquid drawn from container $B$ will be:

$2.1-x$

Now,

$\frac{5x}{8}+\frac{1}{4}(2.1-x)=1.05$

Multiply by $8$:

$5x+2(2.1-x)=8.4$

$5x+4.2-2x=8.4$

$3x=4.2$

$x=1.4$

Therefore, $1.4$ litres should be drawn from container $A$.