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Three liquids A, B and C having same specific heat and mass m, 2m and 3m have temperatures $20^{°} C, 40^{°} C$ and $60^{°} C$ respectively. Temperature of the mixture when
Column - I Column - II
A) A and B are mixed p) ${33.3}^{°} C$
B) A and C are mixed q) $52^{°} C$
C) B and C are mixed r) $50^{°} C$
D) A,B and C all three are mixed s) ${46.67}^{°} C$

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A - r , B - s , C - q , D - p

A - r , B - s , C - p , D - p

A - s , B - p , C - r , D - q

A - p , B - r , C - q , D - s

answer is B.

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Detailed Solution

$A \to p; B \to r; C \to q; D \to s$

A and B : $(m) (s) (θ - 20) = (2 m) (s) (40 - θ)$

or $θ = \frac{100}{3} = {33.3}^{°} C$

A and C: $(m) (s) (θ - 20) = (3 m) (s) (60 - θ)$

$θ = 50^{°} C$

B and C: $(2 m) (s) (θ - 40) = (3 m) (s) (60 - θ)$

$θ = 52^{°} C$

A,B and C: $(m) (s) (θ - 20) + (2 m) (s) (60 - θ)$

$= (3 m) (s) (60 - θ)$

$θ = {46.67}^{°} C$

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