Question

A thermometer in contact with a boiled bathtub shows reading ${x_0}$ and with an ice bath tub shows reading of $\dfrac{{{x_0}}}{3}$ . It shows a reading of $\dfrac{{{x_0}}}{2}$ when bought in contact with a body. What is the temperature of the body?
A. ${25^0}C$
B. ${50^0}C$
C. ${75^0}C$
D. ${33^0}C$

Answer 1

Hint: Thermometer is a device to measure the temperature of a body. The boiling point of water is ${100^0}C$ and the freezing point of water, which is ice, has a temperature of ${0^0}C$ . Here we will use these temperature readings at points of boiled bathtub and ice bathtub in order to calculate the temperature of the body at a reading of $\dfrac{{{x_0}}}{2}$.

Complete step by step answer:
 Let us draw the reading scale of thermometer in which the highest scale reading at ${x_0}$ which is boiled bathtub reading of temperature ${100^0}C$ and the lowest scale reading represented by $\dfrac{{{x_0}}}{3}$ which is temperature of ice bathtub reading of temperature ${0^0}C$ . Now, at the point of reading the body $\dfrac{{{x_0}}}{2}$ , let us assume the temperature of the body is $T$.

Now, in order to calculate the value of ${x_0}$ , we know the difference in temperature between boiled water reading of ${100^0}C$ and the ice water reading of ${0^0}C$ will be equal to difference in readings of both cases which is ${x_0} - \dfrac{{{x_0}}}{3}$ so, we have
${x_0} - \dfrac{{{x_0}}}{3} = 100 - 0$
$\Rightarrow \dfrac{{2{x_0}}}{3} = 100$
$\Rightarrow {x_0} = \dfrac{{300}}{2}$
$\Rightarrow {x_0} = 150 \\ $
Now, we have the value of temperature at ${x_0} = 150$ which is ${100^0}C$ and value of temperature at $\dfrac{{{x_0}}}{2}$ is $T$ so, we can write the temperature difference as:
${x_0} - \dfrac{{{x_0}}}{2} = 100 - T$
Put ${x_0} = 150$ we get,
$150 - 75 = 100 - T$
$\therefore T = 100 - 75$
So, the temperature of the body will be $T = {25^0}C$.

Hence, the correct option is A.

Note: Remember in the thermometer, the highest reading generally taken as the boiling point of water ${100^0}C$ and lowest temperature is taken as freezing point of water ${0^0}C$, and the difference between any two readings is just the difference in temperature between two bodies at their particular readings at thermometer. Another most common measuring unit of temperature is Fahrenheit which is related as $F = \dfrac{9}{5}C + 32$.