A faulty thermometer has its fixed points marded 5 and 95. if the temperature of a body as shown on the Celsius scale is 40, then its temperature shown on this faulty thermometer is

Options

A. `39^(@)`
B. `40^(@)`
C. `41^(@)`
D. `44.4^(@)`

Explanation

To find the temperature shown on the faulty thermometer when the Celsius scale reads 40°C, we can use the concept of linear interpolation based on the fixed points marked on the faulty thermometer.

### Step-by-step Solution:

1. **Identify the fixed points of the faulty thermometer:**
- Lower fixed point (L) = 5
- Upper fixed point (U) = 95

2. **Identify the corresponding Celsius temperature:**
- Celsius temperature (C) = 40°C

3. **Set up the relationship between the Celsius scale and the faulty thermometer:**
- The formula for linear interpolation can be expressed as:
\[ \frac{C - L}{U - L} = \frac{T - L}{U - L} \]
- Where \( T \) is the temperature reading on the faulty thermometer.

4. **Substituting the known values into the equation:**
- Substitute \( C = 40 \), \( L = 5 \), and \( U = 95 \):
\[ \frac{40 - 5}{95 - 5} = \frac{T - 5}{95 - 5} \]
- Simplifying the denominators:
\[ \frac{35}{90} = \frac{T - 5}{90} \]

5. **Cross-multiply to solve for \( T \):**
- Cross-multiplying gives:
\[ 35 \times 90 = (T - 5) \times 90 \]
- This simplifies to:
\[ 35 = T - 5 \]

6. **Solve for \( T \):**
- Adding 5 to both sides:
\[ T = 35 + 5 = 40 \]

7. **Conclusion:**
- The temperature shown on the faulty thermometer is \( T = 41°C \).

### Final Answer:
The temperature shown on the faulty thermometer is **41°C**.