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Q.

The temperature of equal masses of three different liquid $A, B, C and 12^{\circ} C, 18^{\circ} C$ and $28^{\circ} C$ respectively. The temperature when A and B are mixed is $16^{\circ} C$ , when B and C are mixed it is $23^{\circ} C$ . Then the temperature when A and C are mixed is __________

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a

25°C

b

25.2°C

c

22.6°C

d

24.2°C

answer is B.

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Detailed Solution

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When A&B are mixed $θ_{mix} = 16$
${mS}_{A} \times 4 = {mS}_{B} \times 2$
$S_{B} = 2 S_{A}$
When B & C are mixed $θ_{mix} = 23$
$\begin{array}{l} {mS}_{B} \times 5 = S_{C} \times 5 \\ S_{C} = S_{B} = 2 S_{A} \end{array}$
When A & C are mix $θ_{mix} = ? = θ$
$\begin{array}{l} {mS}_{A} (θ - 12) = {mS}_{C} \times (28 - θ) \\ S_{A} (θ - 12) = 2 S_{A} (28 - θ) \\ θ - 12 = 2 \times 28 - 2 θ \\ 3 θ = 56 + 12 \\ θ = \frac{68}{3} \\ θ = 22 {.6}^{\circ} C \end{array}$

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