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

Options

A. 233.15K
B. 40K
C. 98K
D. `-40°C`

Answer

To find the temperature at which both the Celsius (Centigrade) and Fahrenheit thermometers read the same temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Temperature**:
Let the temperature at which both thermometers read the same be denoted as \( x \).

2. **Use the Conversion Formula**:
The relationship between Celsius (C) and Fahrenheit (F) is given by the formula:
\[ F = \frac{9}{5}C + 32 \]
Since we are looking for the temperature where both readings are the same, we can set \( F \) and \( C \) equal to \( x \):
\[ x = \frac{9}{5}x + 32 \]

3. **Rearrange the Equation**:
To solve for \( x \), we can rearrange the equation:
\[ x - \frac{9}{5}x = 32 \]
This simplifies to:
\[ \frac{5}{5}x - \frac{9}{5}x = 32 \]
\[ -\frac{4}{5}x = 32 \]

4. **Solve for \( x \)**:
Multiply both sides by -5 to eliminate the fraction:
\[ 4x = -160 \]
Now, divide by 4:
\[ x = -40 \]

5. **Conclusion**:
Therefore, the temperature at which both the Celsius and Fahrenheit thermometers read the same is:
\[ x = -40 \text{ degrees} \]

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

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