$\frac{\Delta T-h A}{\Delta t}$

where, $\Delta T=$ temperature change $\left(T_{f}-T_{i}\right)$, $\Delta t=$ time interval, $k=$ a constant

depending on shape of bodies, $A=$ surface area and $V=$ volume.

As in given case, bottles are identical and they cool down by same temperatures,

$\Delta t \propto \frac{V}{A}$

$\text { So, } \Delta t \propto \frac{A \cdot h}{A} \text { or } \Delta t \propto h$

$\therefore \quad \frac{t_{A}}{t_{B}}=\frac{h_{A}}{h_{B}} \Rightarrow \frac{t_{A}}{t_{B}}=\frac{h_{A}}{2 h_{A}} \quad\left[\therefore h_{B}=2 h_{A}\right]$

$\Rightarrow \quad t_{B}=2 t_{A}$