If the coefficient of real expansion  ${\gamma }_R$ is 1% more then coefficient of apparent expansion, linear expansion coefficient of the material is

$given {\gamma }_R coefficient of real expansion in 1\% more than {\gamma }_a coefficient of apparent expansion$$\Rightarrow {\gamma }_R={\gamma }_a+\frac{1}{100}{\gamma }_a=\frac{101}{100}{\gamma }_a$

$$\begin{gathered} we know that \\ {\gamma }_R={\gamma }_a+{\gamma }_g \end{gathered}$$

$$\begin{gathered} {\gamma }_R={\gamma }_a+3{\alpha }_{g } \\ substitute {\gamma }_a value here \end{gathered}$$

$$\begin{gathered} {\gamma }_R=\frac{100}{101}{\gamma }_R+3{\alpha }_g \\ 3{\alpha }_g={\gamma }_R\left[1-\frac{100}{101}\right]=\frac{{\gamma }_R}{101} \\ {\alpha }_g=\frac{{\gamma }_R}{303} \end{gathered}$$