The temperature of equal masses of three different liquids A, B and C are `30^@C`, `60^@C` and `75^@C` respectively. The temperature when A and B are mixed is `50^@C` and when B and C are mixed, it is `70^@C`. The equilibrium temeprature when A and C are mixed will be

Options

A. `56^@C`
B. `66^@C`
C. `50^@C`
D. `60^@C`

Answer

B

Explanation

`(A+B):ms_B(60-50)=ms_A(50-30)`
`10s_B=20s_AimpliesS_A=(s_B)/(2)`
`(B+C):ms_C(75-70)=ms_B(70-60)`
`5S_C=10S_BimpliesS_C=2s_B`
`(A+C):ms_C(75-theta)=ms_A(theta-30)`
`2S_B(75-theta)=(S_B)/(2)(theta-30)`
`4(75-theta)=theta-30`
`theta=(330)/(s)=66^@C`