On a temperature scale 'X', the boiling point of water is 65° X and the freezing point is -15° X. Assume that the X scale is linear. The equivalent temperature corresponding to -95° X on the Farenheit scale would be:

Solution

Physics sir · 3 steps

Line the X scale up against Fahrenheit using the same two fixed points, then compare fractions of the range.

1. Set up the ratio. On any linear scale, (reading minus freezing point) divided by (boiling point minus freezing point) is the same for a given temperature. The X scale spans 65 - (-15) = 80 divisions and the Fahrenheit scale spans 212 - 32 = 180 divisions.

   (X - (-15))/(65 - (-15)) = (F - 32)/(212 - 32)

2. Put in numbers. For X = -95, the left side is (-95 + 15)/80 = -80/80 = -1. So F - 32 = -180, which gives F = -148. This is the same as -100°C.
3. So. -95°X corresponds to -148°F, which is option (a).

The idea to keep. For any two linear scales, (reading minus lower fixed point) divided by (upper minus lower fixed point) is equal. Always use each scale's own range, never just shift the reading.

Answer from the NTA final answer key. Solution by PrepWiser.