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

An object kept in a large room having an air temperature of \(25^\circ \text{C}\) takes \(12 ~\text{min}\) to cool from \(80^\circ \text{C}\) to \(70^\circ \text{C}.\) The time taken to cool for the same object from \(70^\circ \text{C}\) to \(60^\circ \text{C}\) would be nearly:
1. \(10 ~\text{min}\)
2. \(12 ~\text{min}\)
3. \(20 ~\text{min}\)
4. \(15 ~\text{min}\)