A cup of coffee cools from $90^\circ C$ to $80^\circ C$ in $t$ minutes, when the room temperature is $20^\circ C$. The time taken by a similar cup of coffee to cool from $80^\circ C$ to $60^\circ C$ at a room temperature same at $20^\circ C$ is:
A $\frac{13}{5}t$
B $\frac{10}{13}t$
C $\frac{5}{13}t$
D $\frac{13}{10}t$