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Question:
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Calculate the temperature which has same numeral value on Celsius and Fahrenheit scale.
Solution:
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Verified Answer
Let us consider $A$ be the value of required temperature having same value an Celsius and Fahrenheit scale. Now, we can write
$$
X^{\circ} \mathrm{F}=X^{\circ} \mathrm{C}=Q
$$
We know that,
$$
\frac{{ }^{\circ} \mathrm{F}-32}{180}=\frac{{ }^{\circ} \mathrm{C}}{100}
$$
Let $\frac{A-32}{180}=\frac{A}{100} \Rightarrow \frac{A-32}{9}=\frac{A}{5}$
$$
\begin{aligned}
&\Rightarrow 5 A-160=9 A \Rightarrow-9 A+5 A=160 \\
&\Rightarrow-4 A=160^{\circ} \Rightarrow A=-40^{\circ} \therefore A=X^{\circ} F=X^{\circ} \mathrm{C}
\end{aligned}
$$
So, $A=-40^{\circ} \mathrm{C}$ or $-40^{\circ} \mathrm{F}$
$$
X^{\circ} \mathrm{F}=X^{\circ} \mathrm{C}=Q
$$
We know that,
$$
\frac{{ }^{\circ} \mathrm{F}-32}{180}=\frac{{ }^{\circ} \mathrm{C}}{100}
$$
Let $\frac{A-32}{180}=\frac{A}{100} \Rightarrow \frac{A-32}{9}=\frac{A}{5}$
$$
\begin{aligned}
&\Rightarrow 5 A-160=9 A \Rightarrow-9 A+5 A=160 \\
&\Rightarrow-4 A=160^{\circ} \Rightarrow A=-40^{\circ} \therefore A=X^{\circ} F=X^{\circ} \mathrm{C}
\end{aligned}
$$
So, $A=-40^{\circ} \mathrm{C}$ or $-40^{\circ} \mathrm{F}$
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