Question

The temperature of which Fahrenheit and Reaumur scale read the same is:
(A) $ - 25.6$
(B) $ - 20.6$
(C) $25.6$
(D) $20.6$

Answer 1

Hint The temperature of which Fahrenheit and Reaumur scale read the same can be determined by the relation between the Fahrenheit and Reaumur scale, and then assume both the Fahrenheit and Reaumur scale as $T$, then the solution can be determined.
Useful formula
The relation between the Fahrenheit and Reaumur scale is given as,
$\dfrac{{F - 32}}{{180}} = \dfrac{R}{{80}}$
Where, $F$ is the Fahrenheit and $R$ is the Reaumur scale.

Complete step by step answer
To find:
When the temperature of which Fahrenheit and Reaumur scale read the same temperature.
Now,
The relation between the Fahrenheit and Reaumur scale is given as,
$\dfrac{{F - 32}}{{180}} = \dfrac{R}{{80}}\,.................\left( 1 \right)$
Assume that the temperature to measure is $T$, so the reading on the Fahrenheit and Reaumur scale will be the temperature of the $T$, then the above equation (1) is written as,
$\dfrac{{T - 32}}{{180}} = \dfrac{T}{{80}}$
By cross multiplying the terms in the above equation, then the above equation is written as,
$80\left( {T - 32} \right) = T \times 180$
By multiplying the terms in the above equation, then the above equation is written as,
$80T - 2560 = 180T$
By rearranging the terms in the above equation, then the above equation is written as,
$180T - 80T = - 2560$
By subtracting the terms in the above equation, then the above equation is written as,
$100T = - 2560$
By rearranging the terms in the above equation, then the above equation is written as,
$T = - \dfrac{{2560}}{{100}}$
By dividing the terms in the above equation, then the above equation is written as,
$T = - 25.6$
The above equation is written as,
$ - {25.6^ \circ }\,F = - {25.6^ \circ }\,R$
Thus, the above equation shows the temperature of which Fahrenheit and Reaumur scale read the same.

Hence, the option (A) is the correct answer.

Note To solve this problem, the students must know the relation of the temperature reading scales. There are different types of the temperature reading scales like Celsius, Fahrenheit, Kelvin and etc, the students must know all the temperature relations.