A cup of coffee cools from $90^{\circ} \mathrm{C}$ to $80^{\circ} \mathrm{C}$ in $\mathrm{t}$ minutes, when the room temperature is $20^{\circ} \mathrm{C}$. The time taken by a similar cup of coffee to cool from $80^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ at a room temperature same at $20^{\circ} \mathrm{C}$ is :
NEET 2021, Medium
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$\frac{d T}{d t}=K\left(T_{a v}-T_{0}\right)$
$\frac{10}{t}=K(85-20)$
$\frac{20}{t}=K(70-20)$
$\frac{t^{\prime}}{2 t}=\frac{65}{50}$
$\frac{t^{\prime}}{t}=\frac{130}{50}$
$t^{\prime}=\frac{13}{5} t$
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