Question

On a hypothetical scale $X$, the ice point is $40^{\circ}$ and the steam point is $120^{\circ}$. For another scale $Y$, the ice point and steam point are $-30^{\circ}$ and $130^{\circ}$ respectively. If $X$ reads $50^{\circ}$, then $Y$ would read :

• A. $-5^{\circ}$
• B. $-8^{\circ}$
• C. $-10^{\circ}$
• D. $-12^{\circ}$

Answer 1

Answer: (C)

We use
$\Rightarrow \frac{50-40}{120-40} =\frac{Y-(-30)}{130-(-30)}$
$\Rightarrow \frac{10}{80} =\frac{Y+30}{160}$
$\Rightarrow \frac{1}{8} =\frac{Y+30}{160}$
$\Rightarrow Y+30 =20$
$\Rightarrow Y =-10^{\circ}$