Question

Three containers $C_1,C_2$ and $C_3$ have water at different temperatures. The table below shows the final temperature $T$ when different amounts of water (given in liters) are taken from each container and mixed (assume no loss of heat during the process)

$C_1$	$C_2$	$C_3$	$T$
$1l$	$2l$	$--$	$60^{o}C$
$--$	$1l$	$2l$	$30^{o}C$
$2l$	$--$	$1l$	$60^{o}C$
$1l$	$1l$	$1l$	$\theta$

The value of $\theta$ (in ${}^{o}C$ to the nearest integer) is___________

Answer 1

Answer: 50

Let ${\theta }_1$ , ${\theta }_2$ and ${\theta }_3$ be the temperatures of water in three containers.
$1{\left(\theta \right)}_1+2{\left(\theta \right)}_2+0{\left(\theta \right)}_3=\left(1+2\right)60$
${\theta }_1+2{\theta }_2=180$ …. (1)
$0\times {\left(\theta \right)}_1+1\times {\left(\theta \right)}_2+2\times {\left(\theta \right)}_3=\left(1+2\right)30$
${\theta }_2+2{\theta }_3=90$ …… (2)
$2\times {\left(\theta \right)}_1+0\times {\left(\theta \right)}_2+1\times {\left(\theta \right)}_3=\left(2+1\right)60$
$2{\theta }_1+{\theta }_3=180$ …. (3)
and ${\left(\theta \right)}_1+{\left(\theta \right)}_2+{\left(\theta \right)}_3=\left(1+1+1\right)\theta$
from (1)+(2)+(3)
$3{\theta }_1+3{\theta }_2+3{\theta }_3=450⟹{\theta }_1+{\theta }_2+{\theta }_3=150$
from (4) equation $150=3\theta ⟹\theta =50^{\circ }C$