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Q. Two temperature scales $A$ and $B$ are related by $\frac{A-42}{110}=\frac{B-72}{220}$. At which temperature two scales have the same reading ?

WBJEEWBJEE 2011Thermal Properties of Matter

Solution:

We are given the relation between the temperature scales $A$ and $B$ as $\frac{A-42}{110}=\frac{B-72}{220}$, so for the two scales to have the same reading $A=B$ and so $\frac{A-42}{110}=\frac{A-72}{220}$, which yields $A=12$.