Question

The temperature reading of a bath on Celsius and Fahrenheit thermometers are in the ratio $2:5$. The temperature of the bath is

• A. $26.67{}^{\circ }\text{C}$
• B. $40.51{}^{\circ }\text{C}$
• C. $45.71{}^{\circ }\text{C}$
• D. $36.66{}^{\circ }\text{C}$

Answer 1

The correct option is C $45.71{}^{\circ }\text{C}$

We know the relation between Celsius and Fahrenheit scale,
$\frac{C}{100}=\frac{F-32}{180}$ ...............(1),
where $C$ is the temperature in Celsius and $F$ is the temperature in Fahrenheit.
Given, $\frac{C}{F}=\frac{2}{5}\Rightarrow F=2.5C$ ............(2)
So, $\frac{C}{100}=\frac{2.5C-32}{180}$
$[$ from (1) and (2) $]$
$\Rightarrow C=\frac{320}{7}\approx {45.71}^{\circ }\text{C}$