Equal masses of three liquids A,B and C are taken. Their initial temperature are `10^@C,25^@C` and `40^@C` respectively. When A and B are mixed the temperature of the mixutre is `19^@C`. When B and C are mixed, the temperature of the mixture is `35^@C`. Find the temperature if all three are mixed.

Explanation

Let the specific heat capacities of A,B,C be `S_1`,`S_2`,`S_3`.
`theta_(A+B)=19=(10S_1+25S_2)/(S_1+S_2)` or `S_1=(2)/(3)S_2`
`theta_(B+C)=35=(25S_2+40S_3)/(S_2+S_3)` or `S_3=2S_2`
`theta_(A+B+C)=(10S_1+25S_2+40S_3)/(S_1+S_2+S_3)`
`=(10xx(2)/(3)S_2+25S_2+40xx2S_2)/((2)/(3)S_2+S_2+2S_2)= 30.5^(@)C`.