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

Options

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

Answer

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

### Step-by-Step Solution:

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

2. **Identify the change in temperature in Celsius:**
We are given that the temperature increases by 30 degrees Celsius. Therefore, we can denote this change as:
\[ \Delta C = 30 \text{ degrees Celsius} \]

3. **Convert the change in temperature from Celsius to Fahrenheit:**
To find the change in temperature in Fahrenheit (\(\Delta F\)), we can rearrange the formula:
\[ \Delta C = \frac{5}{9} \Delta F \]
where \(\Delta F\) is the change in temperature in Fahrenheit.

4. **Substituting the known change in Celsius:**
Substitute \(\Delta C = 30\) into the equation:
\[ 30 = \frac{5}{9} \Delta F \]

5. **Solve for \(\Delta F\):**
To isolate \(\Delta F\), multiply both sides by \(\frac{9}{5}\):
\[ \Delta F = 30 \times \frac{9}{5} \]
\[ \Delta F = 30 \times 1.8 \]
\[ \Delta F = 54 \text{ degrees Fahrenheit} \]

6. **Conclusion:**
The increase in temperature on the Fahrenheit scale is 54 degrees.

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

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