Question

The fundamental intervals of two thermometers X and Y are 70$^\circ$ and 140$^\circ$ respectively. Their ice points are 10$^\circ$ and 0$^\circ$ respectively. If Y reads 90$^\circ$. What would X read?

Answer 1

Hint: Fundamental scale is the difference of readings of two points on a thermometer like ice point and boiling point. We have to find the equivalent readings in case of both the thermometers. This can be treated as the case when we make conversion between Fahrenheit and Celsius scale.

Complete answer:
Let the reading on the thermometer X be x and on the thermometer Y be y, then we need to find a relation between both the thermometer readings. We first subtract the x reading with the respective zero value of the thermometer and the h reading with the respective zero. Zero is marked on both the thermometers with the value given for ice. The ratio of the readings are:
$\dfrac{x - 10}{70} = \dfrac{y - 0}{140}$
It has been given that the Y thermometer reads 90$^\circ$, the reading on the thermometer X can be found with the help of above equation,
$x = 10 + \dfrac{90 \times 70}{140}$
$x = 10 + 45 = 55 ^\circ$ .
Therefore, the reading on the X thermometer reads 55 $^\circ$ when the reading on the thermometer Y reads 90 $^\circ$.

Note:
If we have a reading x on the thermometer X which has a separation of 70$^\circ$ for a set of two points and if we have a separation of 140$^\circ$ for the same set of points on the thermometer Y, we subtract the zero reading from both x and y and then we divide by their temperature difference. If both x and y started from zero, we could have simply said that if the reading on x will show suppose 5, then on y it would be just 2x or 10. Simple ratio proportions have to be followed here.