Given, $T_1=27+273=300 K ;$ $T_2=37+273=310K$

Temperature coefficient of a reaction is ideally = 2.

Let the rate of reaction at $27°C$ be $k$ i.e.  $K_1=k$ , then rate of reaction at $37°C$ be $2k$i.e. $K_2= 2k$
From the Arrhenius equation we get , 
$\Rightarrow \log \frac{{\mathrm{k}}_2}{{\mathrm{k}}_1}=\frac{{\mathrm{E}}_{\mathrm{a}}}{2.303 \mathrm{R}}\left(\frac{{\mathrm{T}}_2-{\mathrm{T}}_1}{{\mathrm{T}}_1{\mathrm{T}}_2}\right)$ , where $E_a$ is the Activation energy & $R=8.314\times {10}^{-3} \mathrm{kJ} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$

$\Rightarrow \log \frac{2k}{k}=\frac{E_a}{2.303 \times 8.314\times {10}^{-3}}\times \left(\frac{310-300}{310\times 300}\right)$

$\Rightarrow \log 2=\frac{E_a}{2.303\times 8.314\times {10}^{-3}}\times \frac{10}{93000}$

$\Rightarrow E_a=\frac{2.303\times 0.3010\times 8.314\times {10}^{-3}\times 93000}{10} kJ mo{l}^{-1}$

$\Rightarrow E_a=53.5 \mathrm{k}\mathrm{J}$