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 solve the problem of finding the temperature of the bath given the readings on Celsius and Fahrenheit thermometers are in the ratio 2:5, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**:
Let the temperature in Celsius be \( T_C \) and the temperature in Fahrenheit be \( T_F \). According to the problem, the ratio of the two temperatures 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**:
We know the relationship between Celsius and Fahrenheit temperatures is given by:
\[ T_F = \frac{9}{5} T_C + 32 \]
We can substitute \( T_F \) from step 2 into this equation:
\[ \frac{5}{2} T_C = \frac{9}{5} T_C + 32 \]

4. **Clear the Fractions**:
To eliminate the fractions, multiply through by 10 (the least common multiple of the denominators):
\[ 25 T_C = 18 T_C + 320 \]

5. **Rearrange the Equation**:
Now, rearranging the equation gives:
\[ 25 T_C - 18 T_C = 320 \]
\[ 7 T_C = 320 \]

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

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

### Final Answer:
The temperature of the bath is approximately **45.71 °C**.

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