ONE GRAM OF STEAM AT 100 DEGREE CELSIUS SENT INTO ONE GRAM OF ICE AT 0 DEGREE CELSIUS THEN FINAL CONDITION OF MIXTURE IS

in this mixing problem

Heat is lost by 100 C steam = Heat gained by 0 C ice

heat gained by ice = m*L_ice+m*S_water*(t_f - 0)

                            = 1*80 + 1*1*t_f

Heat lost by steam = m*L_water + m*S_water *(100 - t_f)

                            = 1*0.5 + 1*1 *(100 - t_f)

t_f = 10.5 C

Note: All Units are in cgs