The temperature of equal masses of three different liquids x, y and...

When $A \text{ and } B$ are mixed

${m}_{1}{S}_{1} ( 16 - 10 ) = {m}_{2}{S}_{2} ( 20 - 16 )$

$6{m}_{1}{S}_{1} = 4{m}_{2}{S}_{2} . . . . . . . ( 1 )$

When $B \text{ and } C$ are mixed

${m}_{2}{S}_{2} ( 26 - 20 ) = {m}_{3}{S}_{3} ( 30 - 26 )$

$6{m}_{2}{S}_{2} = 4{m}_{3}{S}_{3} . . . . . . . . . . . ( 2 )$

From equation $( 1 )$ and $( 2 )$

$9{m}_{1}{S}_{1} = 4{m}_{3}{S}_{3}$

When $A \text{ and } C$ are mixed

${m}_{1}{S}_{1} ( T - 10 ) = {m}_{3}{S}_{3} ( 30 - T )$

$T = \dfrac{30{m}_{3}{S}_{3} + 10{m}_{1}{S}_{1}}{{m}_{1}{S}_{1} + {m}_{3}{S}_{3}}$

$T = \dfrac{10\left(3{m}_{3}{S}_{3} + {m}_{1}{S}_{1}\right)}{{m}_{3}{S}_{3} + {m}_{1}{S}_{1}}$

$T = \dfrac{10\left(3{m}_{3}{S}_{3} + \dfrac{4}{9}{m}_{3}{S}_{3}\right)}{{m}_{3}{S}_{3} + \dfrac{4}{9}{m}_{3}{S}_{3}}$

$T = \dfrac{10 \times 31}{13}$

$= 23 . 84 ° C$