The temperature of equal masses of three different liquids A,B and C are `12^@C, 19^@C and 28^@C` respectively. The temperature when A and B are mixed is `16^@C` and when B and C are mixed it is `23^@C`. What should be the temperature when A and C are mixed?

Options

A. 18.2`""^@` C
B. 22`""^@`C
C. 20.2 `""^@`C
D. 25.2`""^@` C

Answer

C

Explanation

`S_(A) (16-12) = S_B (19-16) rArr (S_A)/(S_B) = (3)/(4)`
`S_B (23 - 19) = S_c (28 - 23) rArr (S_B)/(S_C) = (5)/(4)`
`S_(A)/(S_C) = (15)/(16)`
`S_(A)(theta -12) = S_c(28 - theta)`
`rArr (15)/(16) = (28-theta)/(theta -12) rArr theta = 20.2^@ C`.