The temperature of equal masses of three different liqids A, B, C are 12C, 19C, and 28C respectively. The temperature, when A and B are mixed is 16C and when B and C are mixed is 23C. When will be the temperature when A and C are mixed?

Let a, b and c be the specific heat capacities of liquids A, B and C.

Let the mass of the liquids be m.

When A and B are mixed:

m* a (16-12) = m*b(19- 16)

4a = 3b

When B and C are mixed:

mb (23-19) = mc (28-23)

4b = 5c

Therefore, 16a = 12b = 15c

Let x be the temperature when A and C are mixed

ma (x -12) = mc (28- x)

a/c = 15/16 = (28-x)/(x-12)

15x - 180 = 448 -16x

31x = 628

x = 20.25 degree

Regards

Arun (askIITians forum expert)