On a new scale of temperature (which is linear) and called the $$W$$ scale, the freezing and boiling points of water are $${39^ \circ }W$$  and $${239^ \circ }W$$  respectively. What will be the temperature on the new scale, corresponding to a temperature of $${39^ \circ }C$$  on the celsius scale ?

Solution :
The relation between true scale and new scale of temperature is given by
$$\eqalign{ & {\left( {\frac{{t - LFP}}{{UFP - LFP}}} \right)_{{\text{true}}}} = {\left( {\frac{{t - LFP}}{{UFP - LFP}}} \right)_{{\text{faulty}}}} \cr & \Rightarrow \frac{{{{39}^ \circ }C - {0^ \circ }C}}{{{{100}^ \circ }C - {0^ \circ }C}} = \frac{{t - {{39}^ \circ }W}}{{{{239}^ \circ }W - {{39}^ \circ }W}} \cr & \Rightarrow t = {117^ \circ }W \cr} $$