Let the temperature of surroundings be ${\theta _0}$
By Newton's law of cooling

${{{\theta _1} - {\theta _2}} \over t} = k\left[ {{{{\theta _1} - {\theta _2}} \over 2} - {\theta _0}} \right]$

$\Rightarrow {{70 - 60} \over 5} = k\left[ {{{70 + 60} \over 2} - {\theta _0}} \right]$

$\Rightarrow 2 = k\left[ {65 - {\theta _0}} \right]$

Similarly, ${{60 - 54} \over 5} = k\left[ {{{60 + 54} \over 2} - {\theta _0}} \right]$

$\Rightarrow {6 \over 5} = k\left[ {57 - {\theta _0}} \right]$

By dividing (i) by (ii) we have

${{10} \over 6} = {{65 - {\theta _0}} \over {57 - {\theta _0}}} \Rightarrow {\theta _0} = {45^o}$