On centigrade scale the temperature of a body increases by 30 degrees. The increase in temperature on fahrenheit scale is

Options

A. `50^(@)C`
B. `40^(@)C`
C. `30^(@)C`
D. `54^(@)C`

Answer

To solve the problem of finding the increase in temperature on the Fahrenheit scale when the temperature increases by 30 degrees Celsius, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between Celsius and Fahrenheit:**
The formula that relates Celsius (C) to Fahrenheit (F) is:
\[ C = \frac{5}{9}(F - 32) \]

2. **Set up the initial and final temperatures:**
Let the initial temperature in Celsius be \( C_1 \) and the final temperature be \( C_2 \). The change in temperature in Celsius is given as:
\[ C_2 - C_1 = 30 \text{ degrees} \]

3. **Express the corresponding Fahrenheit temperatures:**
Let the initial temperature in Fahrenheit be \( F_1 \) and the final temperature be \( F_2 \). We can express the temperatures in Fahrenheit using the formula:
- For \( C_1 \):
\[ C_1 = \frac{5}{9}(F_1 - 32) \quad \text{(Equation 1)} \]
- For \( C_2 \):
\[ C_2 = \frac{5}{9}(F_2 - 32) \quad \text{(Equation 2)} \]

4. **Subtract the two equations:**
To find the change in temperature in Fahrenheit, we subtract Equation 1 from Equation 2:
\[ C_2 - C_1 = \frac{5}{9}(F_2 - 32) - \frac{5}{9}(F_1 - 32) \]
Simplifying this gives:
\[ C_2 - C_1 = \frac{5}{9}(F_2 - F_1) \]

5. **Substitute the change in Celsius:**
We know that \( C_2 - C_1 = 30 \):
\[ 30 = \frac{5}{9}(F_2 - F_1) \]

6. **Solve for the change in Fahrenheit:**
Rearranging the equation to find \( F_2 - F_1 \):
\[ F_2 - F_1 = 30 \times \frac{9}{5} \]
Calculating this gives:
\[ F_2 - F_1 = 30 \times 1.8 = 54 \text{ degrees} \]

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

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