The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation C = \(\frac{5F-160}{9}\) What is the numerical value of temperature which is same in both the scale ?
A) 30°
B) -40°
C) 40°
D) -30°
Correct option is (C) 40°
For same temperature in both scale, we have to put C = F in the formula \(C=\frac{5F-160}{9}.\)
\(\therefore\) \(C=\frac{5C-160}{9}\)
\(\Rightarrow\) 9C = 5C - 160
\(\Rightarrow\) 9C - 5C = -160
\(\Rightarrow\) 4C = -160
\(\Rightarrow\) C = \(\frac{-160}{4}\) = 40
Hence, \(40^\circ\) of temperature is same in both the scale.