The readings of a bath on Celsius and Fahrenheit thermometers are in the ratio 2 :5. The temperature of the bath is

Options

A. `-26.66^(@)C`
B. `40^(@)C`
C. `45.71^(@)C`
D. `26.66^(@)C`

Explanation

To find the temperature of the bath in degrees Celsius when the readings on the Celsius and Fahrenheit thermometers are in the ratio 2:5, we can follow these steps:

### Step-by-Step Solution:

1. **Set Up the Ratio**:
Let the temperature in Celsius be \( T_C \) and the temperature in Fahrenheit be \( T_F \). According to the problem, the ratio is given as:
\[ \frac{T_C}{T_F} = \frac{2}{5} \]

2. **Express \( T_F \) in Terms of \( T_C \)**:
From the ratio, we can express \( T_F \) in terms of \( T_C \):
\[ T_F = \frac{5}{2} T_C \]

3. **Use the Conversion Formula**:
The relationship between Celsius and Fahrenheit is given by the formula:
\[ T_F = \frac{9}{5} T_C + 32 \]

4. **Substitute \( T_F \) in the Conversion Formula**:
Substitute the expression for \( T_F \) from step 2 into the conversion formula:
\[ \frac{5}{2} T_C = \frac{9}{5} T_C + 32 \]

5. **Clear the Fractions**:
To eliminate the fractions, multiply the entire equation by 10 (the least common multiple of 2 and 5):
\[ 25 T_C = 18 T_C + 320 \]

6. **Rearrange the Equation**:
Move all terms involving \( T_C \) to one side:
\[ 25 T_C - 18 T_C = 320 \]
\[ 7 T_C = 320 \]

7. **Solve for \( T_C \)**:
Divide both sides by 7:
\[ T_C = \frac{320}{7} \approx 45.71 \]

8. **Conclusion**:
The temperature of the bath is approximately:
\[ T_C \approx 45.71 \text{ °C} \]

### Final Answer:
The temperature of the bath is \( 45.71 \text{ °C} \).

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