Question

The temperature of equal masses of three different liquids $A,B,andC$ are ${10}^{\circ }C,{15}^{\circ }Cand{20}^{\circ }C$ respectively. the temperature when $AandB$ are mixed is ${13}^{\circ }C$ and when $BandC$ are mixed, it is ${16}^{\circ }C$. What will be the temperature when $AandC$ are mixed?

• A. $\frac{20}{11}{}^{\circ }C$
• B. $\frac{20}{3}{}^{\circ }C$
• C. $\frac{140}{11}{}^{\circ }C$
• D. $\frac{140}{3}{}^{\circ }C$

Answer 1

Answer: (C)

$\frac{140}{11}{}^{\circ }C$

When A and B are mixed,

$m{c}_A(13-10)=m{c}_B(15-13)$

$\Rightarrow c_A=2c_B/3-\left(1\right)$

when B and C are mixed,

we get $c_B=4c_C-\left(2\right)$

when A and C are mixed,

$m{c}_A(t-10)=m{c}_C(20-t)$

from $\left(1\right)and\left(2\right)$, $t={\frac{140}{11}}^{o}C$