The temperature at which centigrade and Fahrenheit scales give the same reading, is

The temperature at which centigrade and Fahrenheit scales give the same reading, is
  1. $-40^{\circ}$
  2. $40^{\circ}$
  3. $-30^{\circ}$
  4. $30^{\circ}$

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.

Asked in: MHT CET Full Test 13

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