As water is not stored anywhere. So, volume flow rate of Ganga $=$ volume flow rate of Bhagirathi + volume flow rate of Alaknanda

$\therefore$ By equation of continuity, we have

$\Rightarrow \quad A_g v_g=A_b v_b+A_a v_a \quad \dots(i)$

It is given that area of flow of Ganga, Alaknanda and Bhagirathi are in ratio,

$A_g: A_a: A_b=3: 2: 1$

or $A_g=3 x, A_a=2 x, A_b=x$

Also, ratio of speeds of Bhagirathi and Alaknanda is

$v_b: v_a=1: \frac{3}{2}$

or

$v_b=y, v_a=\frac{3}{2} y$

Substituting these values in Eq. $(i)$, we get

$3 x \cdot v_g=x \cdot y+2 x \cdot \frac{3}{2} y=4 x y$

So,

$v_g=\frac{4}{3} y$

$\therefore$ Ratio of speed of Ganga to that of Alaknanda is

$\frac{v_g}{v_a}=\frac{\frac{4}{3} y}{\frac{3}{2} y}=\frac{8}{9}$