A body is cooled in 2 min in a room at temperature of 30^oC from 75^oC to 65^oC. If the same body is cooled from 55^oC to 45^oC in the same room the time taken (in minute) will be _______.

From $\frac{\left({\mathrm{\theta }}_1-{\mathrm{\theta }}_2\right)}{\mathrm{t}}=\mathrm{\alpha }\left(\frac{{\mathrm{\theta }}_1+{\mathrm{\theta }}_2}{2}-{\mathrm{\theta }}_0\right)$, in the first case we have,

          $\frac{75-65}{2}=\mathrm{\alpha }\left[\frac{75+65}{2}-30\right]$          …(i)

For the second case, 

          $\frac{55-45}{\mathrm{t}}=\mathrm{\alpha }\left[\frac{55+45}{2}-30\right]$           …(ii)

Divide Eq. (i) by Eq. (ii), $\frac{\mathrm{t}}{2}=2$

        $\therefore \mathrm{t}=4\min$