Two liquids at temperature 60° C and 20° C respectively have masses in the ratio 3:4 and the specific heats in the ratio 4:5, if they are mixed the resultant temperature is:

From Principle of method of mixtures,

heat lost by hot liquid = heat gained by cold liquid.

given masses in the ratio=3:4

specific heats in the ratio=4:5

$\begin{array}{rcl}let hot liquid mass & =& 3m, specific heat =4c\\ now cold liquid mass& =& 4m, specific heat =5c\\ heat lost by hot liquid & =& m C∆T=3m\left(4c\right)(60-\theta )\\ heat gain by cold liquid & =& m C∆T=4m\left(5c\right)(\theta -20)\\ & & \\ heat lost by hot liquid & =& heat gain by cold liquid \\ 3m\left(4c\right)(60-\theta )& =& 4m\left(5c\right)(\theta -20)\\ & \Rightarrow & \theta ={35}^{0}C\end{array}$