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

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

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

\(\Rightarrow h=h^{\prime}\)

\(\Rightarrow \frac{h^{\prime}}{h}=1\)