Question

At what temperature do Fahrenheit and Celsius scale give the same reading.
\[
  A.{\text{ - 1}}{{\text{0}}^ \circ }C \\
  B.{\text{ 1}}{{\text{0}}^ \circ }C \\
  C.{\text{ 4}}{{\text{0}}^ \circ }C \\
  D.{\text{ - 4}}{{\text{0}}^ \circ }C \\
\]

Answer 1

Hint: Celsius is also called a centigrade scale which is based on ${0^ \circ }$C for the freezing point of water and ${100^ \circ }$C for the boiling point of water. The Fahrenheit scale takes ${32^ \circ }$F as a freezing point and ${212^ \circ }$F as a boiling point of water.

Complete answer:
Fahrenheit and Celsius are the two scales used to measure the temperature. The temperature in Celsius scale will be expressed in degree Celsius whereas the temperature Fahrenheit scale will be expressed in degree Fahrenheit. The relation between both Fahrenheit and Celsius scales is proportional i-e both are having different freezing points of water and both follow the varied unit difference between each scale.
When the temperature in Celsius scale increases, its Fahrenheit temperature equivalent temperature will also be high. When the temperature in Celsius scale decreases, its Fahrenheit temperature equivalent temperature will also be low. From both Celsius and Fahrenheit scales the C Fahrenheit is the smallest unit of the temperature.
The formula for converting between degree Celsius and degree Fahrenheit are:

$
  ^ \circ F = {(^ \circ }C*9/5) + 32 \\
  ^ \circ C = {(^ \circ }F - 32)*5/9 \\
$

By using the old algebra trick

$
  ^ \circ F{ = ^ \circ }C \\
  { \Rightarrow ^ \circ }C = {(^ \circ }C*9/5) + 32 \\
  { \Rightarrow ^ \circ }C - {(^ \circ }C*9/5) = 32 \\
  \implies - 4/5{*^ \circ }C = 32 \\
  { \Rightarrow ^ \circ }C = - 32*5/4 \\
  { \Rightarrow ^ \circ }C = - 40 \\


   F = {(^ \circ }C*9/5) + 32 \\
  { \Rightarrow ^ \circ }F - {(^ \circ }C*9/5) = 32 \\
  \implies - 4/5{*^ \circ }F = 32 \\
  { \Rightarrow ^ \circ }F = - 32*5/4 \\
  { \Rightarrow ^ \circ }F = - 40 \\
 $

So, the temperature when both the Celsius and Fahrenheit scales are the same as given above.

So, the correct answer is “Option D”.

Note:
Both the scales Celsius and Fahrenheit have their own thermometer for the measurements. Besides these two temperatures, there are two more types of temperature that exist: Kelvin scale and the Rankin scale. Moreover from all the four temperatures the Celsius and Fahrenheit scales are the most commonly used whereas the kelvin is used for scientific experiments.