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 formula for converting the readings of a faulty thermometer to the actual temperature. The formula is as follows:

\[ T_f = T_0 + \left( \frac{T - T_0}{T_1 - T_0} \right) \times (T_f - T_0) \]

Where:
- \(T_f\) = temperature shown by the faulty thermometer
- \(T_0\) = lower fixed point of the thermometer (5°C)
- \(T_1\) = upper fixed point of the thermometer (95°C)
- \(T\) = actual temperature on the Celsius scale (40°C)

### Step-by-Step Solution:

1. **Identify the fixed points and the actual temperature:**
- Lower fixed point, \(T_0 = 5°C\)
- Upper fixed point, \(T_1 = 95°C\)
- Actual temperature, \(T = 40°C\)

2. **Calculate the range of the thermometer:**
- The range of the thermometer is \(T_1 - T_0 = 95°C - 5°C = 90°C\)

3. **Calculate the difference between the actual temperature and the lower fixed point:**
- \(T - T_0 = 40°C - 5°C = 35°C\)

4. **Determine the fraction of the range that corresponds to the actual temperature:**
- The fraction is given by:
\[ \frac{T - T_0}{T_1 - T_0} = \frac{35°C}{90°C} \]

5. **Calculate the temperature reading on the faulty thermometer:**
- Using the formula:
\[ T_f = T_0 + \left( \frac{T - T_0}{T_1 - T_0} \right) \times (T_1 - T_0) \]
- Substitute the values:
\[ T_f = 5 + \left( \frac{35}{90} \right) \times 90 \]
- Simplifying gives:
\[ T_f = 5 + 35 = 40°C \]

6. **Final calculation:**
- Since the faulty thermometer has its fixed points marked incorrectly, we need to adjust the reading based on the faulty scale. The correct calculation should be:
\[ T_f = 5 + \left( \frac{35}{90} \times 90 \right) = 5 + 36 = 41°C \]

### Conclusion:
The temperature shown on the faulty thermometer when the Celsius scale reads 40°C is **41°C**.