Initially at lower end
P = 76cm of Hg + 76cm of air = 152cm
T = 300K
$V = \large\frac{V_1}{2}$
Where $V_1$ is the volume of the cylinder
Finally at lower end
P = 76cm of air + 38cm of Hg = 114 cm
T = ?
$V = \large\frac{3V_1}{4}$
$\therefore \large\frac{P_1V_1}{T_1} = \large\frac{P_2V_2}{T_2}$
$\large\frac{152\times V_1}{2\times300} = \large\frac{114\times3V_1}{4\times T}$
$\therefore T = \large\frac{114\times3\times2\times300}{152\times4}$
= 337.5K
Hence answer is (c)