${\gamma _{mixture}} = {\left( {\frac{{{C_p}}}{{{C_V}}}} \right)_{mix}} = \frac{{\frac{{{n_1}{\gamma _1}}}{{{\gamma _1} - 1}} + \frac{{{n_2}{\gamma _2}}}{{{\gamma _2} - 1}}}}{{\frac{{{n_1}}}{{{\gamma _1} - 1}} + \frac{{{n_2}}}{{{\gamma _2} - 1}}}}$

Putting the value of ${n_1} = 2,{n_2} = n.$

${\left( {\frac{{{C_p}}}{{{C_v}}}} \right)_{mix }} = \frac{3}{2}$

${\gamma _1} = \frac{5}{3},{\gamma _2} = \frac{7}{5}$ and solving we get, $n=2$