An object kept in a large room having air temperature of $25^{\circ} \mathrm{C}$ takes $12$ minutes to cool from $80^{\circ} \mathrm{C}$ to $70^{\circ} \mathrm{C}$. The time taken to cool for the same object from $70^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ would be nearly.....$min$
NEET 2019, Medium
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$\frac{\mathrm{T}_{1}-\mathrm{T}_{2}}{\mathrm{t}}=\mathrm{K}\left(\frac{\mathrm{T}_{1}+\mathrm{T}_{2}}{2}-\mathrm{Ts}\right)$
$\frac{80-70}{12}=\mathrm{K}\left(\frac{80+70}{2}-25\right) \ldots(1)$
$\frac{70-60}{t}=K\left(\frac{70+60}{2}-25\right) \ldots(2)$
on solving $: t=15 \mathrm{min}$
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