Three liquids `A, B` and `C` having same specific heat and mass m , `2`m and `3` m have temperature `20^(@)C , 40^(@)C` and `60^(@)C` respectively. Temperature of the mixture when:
`{:(,"Column-I",,"Column-II"),((A),"A and B are mixed",(p),35^(@)C),((B),"A and C are mixed",(q),52^(@)),((C),"B and C are mixed",(r),50^(@)),((D),"A,B and C all three are mixed",(s),45^(@)),(,,(t),"None"):}`

Answer

A, B, C, D

Explanation

When A and B are mixed together
(m)(c)(`theta-20)` = (2m)(c) `(40^(@)-theta)`
or `theta=100/3 = 33.33^(@)`C
When A and C are mixed together
(m)(c)(`theta`-20)=(3m)(c)`(60^(@)-theta)` or `theta=50^(@)`C
When B and C are mixed together
(2m)(c)(`theta`-40) = (3m)(c)(`60^(@)-theta)rArr theta=52^(@)C`
When A, B and C all are mixed
(m)(c)(`theta`-20)+(2m)(c)(`60^(@)-theta`) = (3m)(c)(`60^(@)-theta)`
or `theta=40^(@)`C