On Celsius scale two temperatures differ by `30^(@)`. What is the difference on Fahrenheit scale?

Explanation

To find the difference in temperature on the Fahrenheit scale when two temperatures differ by 30 degrees Celsius, we can use the formula for converting Celsius to Fahrenheit.

### Step-by-Step Solution:

1. **Understand the conversion formula**: The conversion from Celsius (C) to Fahrenheit (F) is given by the formula:
\[ F = \frac{9}{5}C + 32 \]

2. **Set up the problem**: We know that the difference in temperature on the Celsius scale is 30 degrees. Let's denote the two temperatures in Celsius as \( T_1 \) and \( T_2 \):
\[ T_2 - T_1 = 30^\circ C \]

3. **Convert the temperatures to Fahrenheit**: Using the conversion formula, we can express the temperatures in Fahrenheit:
\[ F_1 = \frac{9}{5}T_1 + 32 \]
\[ F_2 = \frac{9}{5}T_2 + 32 \]

4. **Find the difference in Fahrenheit**: The difference in Fahrenheit can be calculated as:
\[ F_2 - F_1 = \left(\frac{9}{5}T_2 + 32\right) - \left(\frac{9}{5}T_1 + 32\right) \]

5. **Simplify the equation**: The constants (32) cancel out:
\[ F_2 - F_1 = \frac{9}{5}T_2 - \frac{9}{5}T_1 \]
\[ F_2 - F_1 = \frac{9}{5}(T_2 - T_1) \]

6. **Substitute the difference in Celsius**: We know that \( T_2 - T_1 = 30 \):
\[ F_2 - F_1 = \frac{9}{5} \times 30 \]

7. **Calculate the difference**:
\[ F_2 - F_1 = \frac{9 \times 30}{5} = \frac{270}{5} = 54 \]

8. **Conclusion**: The difference in temperature on the Fahrenheit scale is:
\[ F_2 - F_1 = 54^\circ F \]

### Final Answer:
The difference in temperature on the Fahrenheit scale is **54 degrees Fahrenheit**.