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

Heat gain = heat lost
`C_(A)(16-12)=C_(B)(19-16) rArr (C_(A))/(C_(B))=(3)/(4)`
and `C_(B)(23-19)=C_(c )(28-23) rArr (C_(B))/(C_(C ))=(5)/(4)`
`rArr (C_(A))/(C_(C ))=(15)/(16)" " …(i)`
If `theta` is the temperature when A and C are mixed then,
`C_(A)(theta-12)=C_(C )(28-theta) rArr =(C_(A))/(C_(C ))=(28-theta)/(theta-12)" "...(ii)`
On solving equations (i) and (ii) `theta=20.2^(@)C`