Q 11-10-094JEE MainJEE Main 2021 (26 Aug, Shift 2)Medium
The temperature of equal masses of three different liquids $x$, $y$ and $z$ are $10^\circ$C, $20^\circ$C and $30^\circ$C respectively. The temperature of mixture when $x$ is mixed with $y$ is $16^\circ$C and that when $y$ is mixed with $z$ is $26^\circ$C. The temperature of mixture when $x$ and $z$ are mixed will be:
Answer: (D) $23.84^\circ$C
Equal masses, so heat lost = heat gained gives:
$x$ and $y$: $s_x(16 - 10) = s_y(20 - 16) \Rightarrow s_x : s_y = 2 : 3$
$y$ and $z$: $s_y(26 - 20) = s_z(30 - 26) \Rightarrow s_y : s_z = 2 : 3$
So $s_x : s_y : s_z = 4 : 6 : 9$. Mixing $x$ and $z$:
$$4(T - 10) = 9(30 - T) \Rightarrow 13T = 310 \Rightarrow T \approx 23.84^\circ\text{C}$$
Solution by Sreeraj P, M.Sc Physics