For hole ' $A$ '

Velocity of efflux $=\sqrt{2 g\left(x+h^{\prime}\right)}$

$R=2\left[\left(x+h^1\right) h\right]^{1 / 2} \quad \ldots (1)$

For hole ' $B$ '

Velocity of efflux $=\sqrt{2 g h^{\prime}}$

$R=2\left[h^{\prime}(x+h)\right]^{1 / 2} \quad \ldots (2)$

Equating $(a)$ and $(b)$

We get

$2\left[\left(x+h^{\prime}\right) h\right]^{1 / 2}=2\left[h^{\prime}(x+h)\right]^{1 / 2}$

$\Rightarrow \left(x+h^{\prime}\right) h=h^{\prime}(x+h)$

$\Rightarrow h=h^{\prime}$

$\Rightarrow \frac{h^{\prime}}{h}=1$