The tempeature at which both centigrade and Fahrenheit thermometer will read same temperature is

Options

A. `273^(@)`
B. `-273^(@)`
C. `0^(@)`
D. `-40^(@)`

Explanation

To find the temperature at which both the Celsius and Fahrenheit scales read the same, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between Celsius and Fahrenheit**:
The formula to convert Celsius (°C) to Fahrenheit (°F) is given by:
\[ F = \frac{9}{5}C + 32 \]
Rearranging this, we can express Celsius in terms of Fahrenheit:
\[ C = \frac{5}{9}(F - 32) \]

2. **Set Celsius equal to Fahrenheit**:
We want to find the temperature (let's call it \( X \)) where both scales are the same:
\[ X = \frac{5}{9}(X - 32) \]

3. **Multiply through by 9 to eliminate the fraction**:
\[ 9X = 5(X - 32) \]
This simplifies to:
\[ 9X = 5X - 160 \]

4. **Rearrange the equation**:
Move all terms involving \( X \) to one side:
\[ 9X - 5X = -160 \]
\[ 4X = -160 \]

5. **Solve for \( X \)**:
Divide both sides by 4:
\[ X = -40 \]

6. **Conclusion**:
The temperature at which both the Celsius and Fahrenheit thermometers read the same is \( -40 \) degrees.

### Final Answer:
The temperature at which both Celsius and Fahrenheit thermometers read the same is **-40 degrees**.