Question

The fundamental interval of a thermometer \[x\] is arbitrarily divided into 40 equal and that of another thermometry into 80 equal parts. If the freezing point of $x$ is marked ${20^ \circ}C$ and that of y is marked ${0^ \circ}C$. What is the temperature on x when y indicates ${70^ \circ}C$? What is the temperature in $^ \circ C$?

Answer 1

Hint: We know that the fundamental interval refers to the value of the difference in temperature between two fixed points on a temperature scale which is taken in order to define the scale. It is also defined as the difference between the values recorded in a thermometer at two fixed points.

Complete answer: We have been given in this question that x is divided arbitrarily into forty equal parts and eighty equal parts in another thermometer, which means one degree rise in temperature on x means the two degree rise in temperature of y. After that also if a temperature is marked zero degrees in y and twenty degrees in x then x is twenty steps ahead of y.
Therefore, ${70^ \circ}C$ in y means ${35^ \circ}C$ in x
Now as x is twenty steps ahead of y, 35 becomes 55
Hence, the correct solution is ${55^ \circ }C$.

Note: One point to be noted is to do the correct visualization of the fact that one degree rise in temperature of x leads to two leads to two degree rise in temperature of y. This should be properly interpreted so one is prone to make mistakes in this.