Let the temperature is t that gives same reading$=\text{t°C}$  

In celsius & Fahrenheit scale$=\text{t°F}$

We know

i)$\text{F}=\frac{\text{9C}}{\text{5}}+32$

$\text{t}=\frac{\text{9t}}{\text{5}}+32$

$\text{5t}=9\text{t}+160$

$-160=9\text{t}-5\text{t}$

$\Rightarrow 4\text{t}=-160$

$\therefore \text{t}=-40°\text{C}=-40°\text{F}$

ii) or consider

$\text{C}=\frac{5}{9}\left(\text{F}-32\right)$

$\text{t}=\frac{5}{9}\left(\text{t}-32\right)$

$9\text{t}=5\text{t}-160$

$4\text{t}=-160$

$\therefore \text{t}=-40°\text{F}$