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

Answer 1

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

We know the relation between Celsius and Fahrenheit scale,

$\frac{C}{100}=\frac{F-32}{180}.......\left(1\right)$,

where $C$ is the temperature in Celsius and $F$ is the temperature in Fahrenheit.

Given, $\frac{C}{F}=\frac{2}{5}$

$\Rightarrow F=2.5C........\left(2\right)$

So,
$\frac{C}{100}=\frac{2.5C-32}{180}[$ from $\left(1\right)$ and $\left(2\right)$ $]$

$\Rightarrow C=\frac{320}{7}\approx {45.71}^{\circ }\text{C}$

Hence, option $\left(\text{C}\right)$ is the right choice.