» » » At what temperature will the Celsius scale coincide with the Fahrenheit scale?

# At what temperature will the Celsius scale coincide with the Fahrenheit scale?

### Question

At what temperature will the Celsius scale coincide with the Fahrenheit scale?

### Options

A)
4$$^{\circ}$$
B)
-273$$^{\circ}$$
C)
100$$^{\circ}$$
D)
-40$$^{\circ}$$

### Explanation:

The relation between the Fahrenheit and Celsius scales is given by the equation.
⇒($$^{\circ}$$F−32) 180 = $$^{\circ}$$C 100

Now, let us assume that Fahrenheit and Celsius scales coincide at x$$^{\circ}$$
Therefore,
⇒(x$$^{\circ}$$−32) 180 = x$$^{\circ}$$ 100
ON solving,
We get,
⇒59(x$$^{\circ}$$−32) = x$$^{\circ}$$
Therefore,
⇒x=−40$$^{\circ}$$
Therefore, Celsius and Fahrenheit scale coincide at -40 degrees.

## Discussion (2)

• The relation between the Fahrenheit and Celsius scale is given by the equation.
⇒(∘F−32)180=∘C100

Now, let us assume that Fahrenheit and Celsius scale coincide at x∘
Therefore,
⇒(∘x−32)180=∘x100
ON solving,
We get,
⇒59(∘x−32)=∘x
Therefore,
⇒x=−40∘
Therefore, Celsius and Fahrenheit scale coincide at -40 degrees.