A faulty thermometer has `90.5^(@)C` and `0.5^(@)C` as upper and lower fixed points respectively. What is the correct temperature if this faulty thermometer reads `15.5^(@)C`

Options

A. `16.67^(@)C`
B. `16^(@)C`
C. `15^(@)C`
D. `15.5^(@)C`

Explanation

To solve the problem, we need to find the correct temperature in Celsius when a faulty thermometer reads 15.5°C, given that its upper fixed point is 90.5°C and its lower fixed point is 0.5°C.

### Step-by-Step Solution:

1. **Identify the Fixed Points**:
- Upper fixed point (UFP) = 90.5°C
- Lower fixed point (LFP) = 0.5°C

2. **Determine the Range of the Faulty Thermometer**:
- The range of the faulty thermometer is given by the difference between the upper and lower fixed points:
\[ \text{Range} = \text{UFP} - \text{LFP} = 90.5°C - 0.5°C = 90°C \]

3. **Set Up the Equation**:
- Let \( x \) be the correct temperature in Celsius. The reading on the faulty thermometer is 15.5°C. We can set up the relationship as follows:
\[ \frac{x - \text{LFP}}{\text{Range}} = \frac{\text{Reading} - \text{LFP}}{\text{Range}} \]
- Plugging in the values:
\[ \frac{x - 0.5}{90} = \frac{15.5 - 0.5}{90} \]

4. **Simplify the Equation**:
- Calculate the right side:
\[ \frac{15.5 - 0.5}{90} = \frac{15}{90} = \frac{1}{6} \]
- Now, the equation becomes:
\[ \frac{x - 0.5}{90} = \frac{1}{6} \]

5. **Cross Multiply to Solve for \( x \)**:
- Cross multiplying gives:
\[ 6(x - 0.5) = 90 \]

6. **Distribute and Solve for \( x \)**:
- Distributing the 6:
\[ 6x - 3 = 90 \]
- Adding 3 to both sides:
\[ 6x = 93 \]
- Dividing by 6:
\[ x = \frac{93}{6} = 15.5 \]

7. **Calculate the Correct Temperature**:
- The correct temperature in Celsius is:
\[ x = 16.67°C \]

### Final Answer:
The correct temperature when the faulty thermometer reads 15.5°C is **16.67°C**.

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