The apparent coefficient of expansion of a liquid when heated in a copper vessel is C and when heated in a silver vessel, it is S. If A is the linear coefficient of expansion of copper, then the linear coefficient of expansion of silver is

${\gamma }_r={\gamma }_a+{\gamma }_v$, where ${\gamma }_r$= coefficient of real expansion,
${\gamma }_{\alpha }$ = coefficient of apparent expansion
and ${\gamma }_v$ = coefficient of expansion of vessel.

For copper, ${\gamma }_r = C + 3{\alpha }_{Cu}= C + 3A$

For silver,    ${\gamma }_r = S + 3{\alpha }_{Ag}$

$\Rightarrow C + 3A = S + 3{\alpha }_{Ag}$

$\Rightarrow {\alpha }_{Ag} = \frac{C - S + 3A}{3}$