The temp of equal masses of three different liquids A, BandC are 12°C, 19°Cand 28°Crespectively. The temp when A and B are mixed is 16°C, and when Band C are mixed is 23°C. The temp when A and C are mixed is

19.1°C

Explanation:

If A and B mix to give 16°C, A has risen by 4°C and B has fallen by 3°C;

If B and C mix to give 23°C, B has risen by 3°C and C has fallen by 5°C;

This means the energy transfered to cause a change of 3°C in B causes a change of 4°C in A and 5°C in C;

We can use this as a ratio (4:5);

The temperature difference between A and C is 16°C;

we add the two parts of the ratio (4+5) to get 9 and divide the temperature difference to get 16/9;

Next we multiply this by one of the parts of the ratio, so with 4, you get 64/9;

This number is the proportional temperature change in A upon mixing;

We then add this to the original temperature of A to get the resultant temperature of the mix like so:

64/9 + 12 = 19.1111 ...

You can do this alternatively using the other part of the ratio;

We would multiply the 16/9 by the 5 instead of the 4 to get 80/9;

This number is the proportional change in temperature in C upon mixing

Then subtract this from this from the original temperature of C and you should get the same answer:

28 - 80/9 = 19.1111 ...