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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\(^{\circ}\)

The correct answer is D.

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.


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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.

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  • Shallom

    How is the answer -40

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