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NCERT Exemplar · Q16

Q.Calculate the temperature which has same numeral value on celsius and Fahrenheit scale.

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We find the temperature where the numerical value is identical on both scales by setting C=FC = F in the conversion formula. The answer is −40°.


The Celsius and Fahrenheit scales measure the same physical quantity—temperature—but use different reference points and step sizes. The Celsius scale sets water's freezing point at 0° and boiling at 100°, while Fahrenheit uses 32° and 212° for the same landmarks. This means the scales diverge everywhere except at one special crossing point.

The conversion formula connecting them is:

F=95C+32F = \frac{9}{5}C + 32

or equivalently,

C=59(F−32)C = \frac{5}{9}(F - 32)

We want the temperature where the number is the same on both thermometers—that is, where C=FC = F numerically. Let's call this common value xx.


Step-by-step solution:

  1. Set up the equation. If the numerical value is the same, then C=F=xC = F = x. Substitute into the conversion formula:

x=95x+32x = \frac{9}{5}x + 32

  1. Isolate xx. Subtract 95x\frac{9}{5}x from both sides:

x−95x=32x - \frac{9}{5}x = 32

Combine the terms on the left. Write xx as 55x\frac{5}{5}x:

55x−95x=32\frac{5}{5}x - \frac{9}{5}x = 32

−45x=32-\frac{4}{5}x = 32

  1. Solve for xx. …

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