In a new scale of temperature the lower fixed point is marked as 0 corresponding to the melting point of a substance which is equal to `25^(@)C` and the upper fixed point is marked corresponding to the boiling point of a substance which is equal to `75^(@)C` The total length of the scale between the UFP and LFP is divided into 200 equal parts. Determine the temperature in the new scale when the temperature of a substance measured by a celsius scale thermometer is `50^(@)C`

Explanation

To solve the problem, we need to convert the temperature from the Celsius scale to the new temperature scale defined by the given fixed points. Here’s a step-by-step solution:

### Step 1: Identify the fixed points
- The lower fixed point (LFP) is at the melting point of a substance, which corresponds to \( 25^\circ C \) and is marked as \( 0 \) in the new scale.
- The upper fixed point (UFP) is at the boiling point of a substance, which corresponds to \( 75^\circ C \) and is marked as \( 200 \) in the new scale.

### Step 2: Calculate the range of the new scale
- The range of the new scale is the difference between the UFP and LFP:
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