Explanation

(c) Ist case
$ms_{A}\left( t - t_{A} \right) = ms_{B}(t_{B} - t)$
$s_{A}(16 - 12) = s_{B}(19 - 16)$
$4s_{A} = 3s_{B}$
IInd case
$ms_{B}\left( t - t_{B} \right) = ms_{C}(t_{C} - t)$
$s_{B}(23 - 19) = s_{C}(28 - 23)$
$4s_{B} = 5s_{C}$
$3s_{B} = \frac{15}{4}s_{C}$
$\therefore$ $4s_{A} = 3s_{B} = \frac{15}{4}s_{C}$
$\Rightarrow$ $16s_{A} = 12s_{B} = 15s_{C} = k$
$s_{A}:s_{B}:s_{C} = \frac{1}{16}:\frac{1}{12}:\frac{1}{15}$
$s_{A} = \frac{k}{16}$ , $s_{C} = \frac{k}{15}$
When A and C are mixed
$ms_{A}\left( t - t_{A} \right) = ms_{C}(t_{C} - t)$
$\frac{k}{16}(t - 12) = \frac{k}{15}(28 - t)$
$15t - 180 = 448 - 16t$
$\ \ \ \ \ \ \ \ \ \ \ \ \ 31t = 628$
$\Rightarrow$ $t = 20.2℃$