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Two thermometers $X$ and $Y$ have ice points marked at $15 °$ and $20 °$ and steam points marked as $75 °$ and $100 °$ respectively. When thermometer $X$ measures the temperature of a bath as $60 °$ on it, what would thermometer $Y$ read when it is used to measure the temperature of the same bath ?

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$75 °$

$80 °$

$90 °$

$60 °$

answer is C.

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Detailed Solution

For any temperature scale

$\frac{R e a d i n g - i c e p o i n t}{S t e a m p o i n t - i c e p o i n t} = c o n s \tan t$

For $X$ and $Y$

$\frac{60 - 15}{75 - 15} = \frac{Y - 20}{100 - 20}$

$\frac{45}{60} = \frac{Y - 20}{80}$

$\frac{3600}{60} = Y - 20$

$60 = Y - 20$

$Y = 80 °$

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