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We know the relation between °F and °C scale
°F = (9/5)°C + 32................(i)
Let the temperature will be x at which both the celsius and fahrenheit scales read the same value.
Putting x in place of °F and °C scale in (i) equation:
x = 9/5 (x) + 32
x - 32 = 9x/5
5x - 160 = 9x
4x = -160
x = -40
So at -40°, both celsius and fahrenheit scales read the same value.
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