A temperature interval has no zero offset

A linear thermometer reads 20°X at 0°C and 170°X at 100°C. During an experiment its reading increases from 50°X to 80°X.

What is the temperature increase in kelvins?

Organize the givens & assumptions

0°C ↔ 20°X
100°C ↔ 170°X
Reading change: 50°X → 80°X

The thermometer response is linear over the stated range; calibration points are exact within this model. The question asks an interval, not an absolute temperature.

A $20\ \mathrm K$
B $30\ \mathrm K$
C $293.15\ \mathrm K$
D $40\ \mathrm K$

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