Equal masses of three liquids A, B and C have temperature `10^(@)C, 25^(@)C` and `40^(@)c` respectively. If A and B are mixed, the mixture has a temperature of `15^(@)C`. If B and C are mixed, the mixture has a temperature of `30^(@)C`, if A and C are mixed will have a temperature of

Options

A. `16^(@)C`
B. `20^(@)C`
C. `25^(@)C`
D. `29^(@)`

Explanation

When system of masses `m_(1),m_(2)…..,` specific heat capacities `s_(1),s_(2)……,`and initial temperature `0_(1),0_(2),....` are mixed, the temperature of the mixture is
`0=(summs0)/(summs)=(m_(1)s_(1)0_(1)+m_(2)s_(2)0_(2)+....)/(m_(1)s_(1)+m_(2)s_(2)+....)`
For system of equal mass, `0=(sums0)/(sums).`
Let `s_(1),s_(2)` and `s_(3)` be the specific heat copacities of
A, B and C respectively.
For `A+B,15=(10s_(1)+25s_(2))/(s_(1)+s_(2))`
or `5s_(1)=10s_(2)` or `s_(1)=2s_(2)`