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?

Answer

`20.3^(@)C`

Explanation

When `A` & `B` are mixed `mS_(A)12 + mS_(B)19 = m(S_(A) + S_(B)) 16 implies 3S_(B) = 4S_(A) …(i)`
When B & C are mixed `mS_(B)19 + mS_(C)28 = m(S_(B) + S_(C)) 23 implies 4S_(B) = 5S_(C) ….(ii)`
when A & C are mixed `mS_(A)12 + mS_(C)28 = m(S_(A) + S_(C)) theta implies theta = 20.3^(@)C`