Q131 / 180 · COMEDK 2015 · Physics
The temperature at which centigrade and Fahrenheit scales give the same reading, is
- Correct answerA$-40^{\circ}$
- B$40^{\circ}$
- C$-30^{\circ}$
- D$30^{\circ}$
Solution
Using relation,
$$
\frac{F-32}{180}=\frac{C}{100} \quad \text{...(i)}
$$
If $F=C=x$, then substituting value of $\mathrm{Eq}$. (i), we get
$$
\begin{array}{ll}
\Rightarrow & \frac{x-32}{180}=\frac{x}{100} \Rightarrow \frac{x}{5}=\frac{x-32}{9} \\
\Rightarrow & 9 x=5 x-160 \Rightarrow 160=-4 x \\
\therefore & x=-40^{\circ}
\end{array}
$$
This is the required temperature at which centigrade and Fahrenheit scale give same reading.
Hence, the correct answer is option: 'A'.