A platinum resistance thermometer has a resistance of $20 \Omega$ at $0^\circ C$ and $25 \Omega$ at $100^\circ C$. If its resistance is measured to be $24 \Omega$ when placed in a hot bath, what is the temperature of the bath, assuming a linear relationship between resistance and temperature?

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?