The temperature of equal masses of three different liquids. A, B and C are 12°C, 19°C and 28°C respectively. The temperature when A and B are mixed is 16°C and when B and C are mixed it is 23°C . What should be the temperature when A and C are mixed?

When liquids A and B are mixed
$\begin{array}{l}{\mathrm{Ms}}_{\mathrm{A}}(16-12):{\mathrm{Ms}}_{\mathrm{B}}(19-16)\\ 4{\mathrm{s}}_{\mathrm{A}}=3{\mathrm{s}}_{\mathrm{B}}\Rightarrow {\mathrm{s}}_{\mathrm{B}}=\frac{3}{4}{\mathrm{s}}_{\mathrm{A}}\to \left(1\right)\end{array}$
When liquids B and C are mixed
$\begin{array}{r}{\mathrm{Ms}}_{\mathrm{B}}(23-19)={\mathrm{Ms}}_{\mathrm{c}}(28-23)\\ 4{\mathrm{s}}_{\mathrm{B}}=5{\mathrm{s}}_{\mathrm{C}}\Rightarrow {\mathrm{s}}_{\mathrm{B}}=\frac{5}{4}{\mathrm{s}}_{\mathrm{C}}\to \left(2\right)\end{array}$
From (1) and (2)
$\frac{4}{3}{\mathrm{S}}_{\mathrm{A}}=\frac{5}{4}{\mathrm{S}}_{\mathrm{C}}\Rightarrow {\mathrm{S}}_{\mathrm{A}}=\frac{5}{4}\times \frac{3}{4}{\mathrm{S}}_{\mathrm{C}}=\frac{15}{16}{\mathrm{S}}_{\mathrm{C}}$
When liquids A and C are mixed
$\begin{array}{l}{\mathrm{ms}}_{\mathrm{A}}\left({\mathrm{t}}_{\mathrm{R}}-12\right)={\mathrm{ms}}_{\mathrm{C}}\left(28-{\mathrm{t}}_{\mathrm{R}}\right)\\ \frac{15}{16}{\mathrm{s}}_{\mathrm{c}}\left({\mathrm{t}}_{\mathrm{R}}-12\right)={\mathrm{s}}_{\mathrm{C}}\left(28-{\mathrm{t}}_{\mathrm{R}}\right)\\ 15\left({\mathrm{t}}_{\mathrm{R}}-12\right)=16\left(28-{\mathrm{t}}_{\mathrm{R}}\right)\\ 15{\mathrm{t}}_{\mathrm{R}}-180=448-16{\mathrm{t}}_{\mathrm{R}}\\ {\mathrm{t}}_{\mathrm{R}}=\frac{628}{31}=20{.25}^{\circ }\mathrm{C}\end{array}$