A faulty thermometer has ice point at `-5^circC` and steam point at `105^circC ` What would be the tempareture shown by this thermometer of a person?(Assume correct tempareture of person is `37^circC`)

Options

A. `42^circC`
B. `32^circC`
C. `35.7^circC`
D. `47^circC`

Answer

To solve the problem, we need to determine the temperature shown by a faulty thermometer when the actual temperature of a person is 37°C. The thermometer has an ice point at -5°C and a steam point at 105°C.

### Step-by-Step Solution:

1. **Identify the given values:**
- Ice point (lower limit, LL) = -5°C
- Steam point (upper limit, UL) = 105°C
- Actual temperature of the person (TC) = 37°C

2. **Set up the formula for conversion:**
The formula to convert the actual temperature to the reading of the faulty thermometer is:
\[ \frac{TC - LL}{UL - LL} = \frac{T - LL}{UL - LL} \]
where \(T\) is the temperature shown by the thermometer.

3. **Substitute the known values into the formula:**
\[ \frac{37 - (-5)}{105 - (-5)} = \frac{T - (-5)}{105 - (-5)} \]
Simplifying the left side:
\[ \frac{37 + 5}{105 + 5} = \frac{T + 5}{110} \]
This gives:
\[ \frac{42}{110} = \frac{T + 5}{110} \]

4. **Cross-multiply to eliminate the fraction:**
\[ 42 = T + 5 \]

5. **Solve for \(T\):**
\[ T = 42 - 5 \]
\[ T = 37 \]

6. **Conclusion:**
The temperature shown by the faulty thermometer when the actual temperature of the person is 37°C is:
\[ T = 37°C \]

### Final Answer:
The temperature shown by the faulty thermometer is **35.7°C**.