+1 vote
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The temperature $T$ in a room varies as a function of the outside temperature $T_0$ and the number of persons in the room $p$, according to the relation $T=K(\theta p +T_0)$, where $\theta$ and $K$ are constants. What would be the value of $\theta$ given the following data?
$$\begin{array}{|c|c|c|} \hline \textbf{T_0} & \textbf {p} &\textbf {T} \\\hline \text{25} & \text{2} & \text{32.4} \\\hline \text{30} & \text{5} & \text{42.0} \\\hline \end{array}$$

1. 0.8
2. 1.0
3. 2.0
4. 10.0

edited | 153 views
Migrated from GO Civil 7 months ago by Arjun

+1 vote

$T=K(\theta \cdot p +T_0)$

• $32.4=K(2\theta +25)\qquad \to (1)$
• $42.0=K(5\theta +30)\qquad \to (2)$

Divide the equation $(1)$ by equation $(2),$ and we get

$\dfrac{32.4}{42.0}=\dfrac{K(2\theta +25)}{K(5\theta +30)}$

$\implies\dfrac{324}{420}=\dfrac{2\theta +25}{5\theta +30}$

$\implies\dfrac{27}{35}=\dfrac{2\theta +25}{5\theta +30}$

$\implies 27(5\theta +30)=35(2\theta +25)$

$\implies 135\theta +810=70 \theta +875$

$\implies 135\theta -70 \theta =875-810$

$\implies 65\theta = 65$

$\implies \theta = 1$

So, correct answer is $(B).$

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