The temperature of equal masses of three different liquids `A, B`, and `C` are `10^(@)C`, `15^(@)C` and `20^(@)C` respectively. The temperature when `A` and `B` are mixed is `13^(@)C` and when `B` and `C` are mixed. It is `16^(@)C`. What will be the temperature when `A` and `C` are mixed?

Explanation

when A and B are mixed
`mS_(1)xx(13-10)=mxxS_(2)xx(15-13)`
`3S_(1)=2S_(2)" "...(1)`

when B and C are mixed
`S_(2)xx1=S_(3)xx4" "...(2)`
when C and A are mixed
`S_(1)(theta-10)=S_(3)xx(20-theta)" "...(3)`
by using equation (1), (2) and (3) we get `theta=(140)/(11).^(@)C`