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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?

Thermal Properties of Matter

Solution:

Let at temperature $T$ both the scales $A$ and $B$ have the same reading.
$\therefore \frac{T-42}{110}=\frac{T-72}{220}$ or
$2 T-84=T-72$ or $T=+12^{\circ}$