Equal masses of three liquids A, B and C have temperatures $10°$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, the temperature of the mixture is
Answer: (A) $16°$C
Concept. Equal masses, so heat balance involves only the specific heats: $s_{\text{hot}}\Delta\theta_{\text{hot}} = s_{\text{cold}}\Delta\theta_{\text{cold}}$.
Step 1. A and B. $s_A(15 - 10) = s_B(25 - 15) \Rightarrow s_A = 2s_B$.
Step 2. B and C. $s_B(30 - 25) = s_C(40 - 30) \Rightarrow s_B = 2s_C$, so $s_A = 4s_C$.
Step 3. A and C.
$$4s_C(\theta - 10) = s_C(40 - \theta) \;\Rightarrow\; 5\theta = 80 \;\Rightarrow\; \theta = 16°\text{C}$$
Answer. $16°$C (Option A).
Solution by Sreeraj P, M.Sc Physics