Question

A thermometer graduated according to a linear scale reads a value $x_0$, when in contact with boiling water, and $\frac{x_0}{3}$, when in contact with ice. What is the temperature of an object in ${}^{\circ }\text{C}$, if this thermometer , in the contact with an object, reads $\frac{x_0}{2}$?

• A. $25$
• B. $35$
• C. $40$
• D. $60$

Answer 1

The correct option is A $25$

Let the temperature of the object is $T^{\circ }\text{C}$



$\Rightarrow T^{\circ }\text{C}=\frac{x_0}{2}-\frac{x_0}{3}=\frac{x_0}{6}$

Also, $\frac{(x_0-\frac{x_0}{3})}{100-0}=\frac{(x_0-\frac{x_0}{2})}{100-T}$

$\Rightarrow 400-4T=300$

$\therefore T={25}^{\circ }\text{C}$

Hence, $\left(A\right)$ is the correct answer.