The relation between the temperature readings of the Celsius (C) and Fahrenheit (F) scales is given by : F = `(9)/(5)C + 32` . If the temperature in Fahrenheit increase by 36 degrees , what is the corresponding increase in the Celsius scale ?

Options

A. `12^(@)`
B. `20^(@)`
C. `32^(@)`
D. `52^(@)`

Answer

To find the corresponding increase in the Celsius scale when the temperature in Fahrenheit increases by 36 degrees, we can follow these steps:

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

### Step 2: Rearrange the formula to express C in terms of F
We can rearrange the formula to express C in terms of F:
\[ F - 32 = \frac{9}{5}C \]
\[ C = \frac{5}{9}(F - 32) \]

### Step 3: Determine the initial temperature in Fahrenheit
Let’s consider an initial temperature in Fahrenheit. A common reference point is:
\[ F = 32 \text{ degrees Fahrenheit} \]
At this point, we can find the corresponding Celsius temperature:
\[ C = \frac{5}{9}(32 - 32) = \frac{5}{9}(0) = 0 \text{ degrees Celsius} \]

### Step 4: Calculate the new temperature in Fahrenheit
Now, if the temperature in Fahrenheit increases by 36 degrees, the new temperature in Fahrenheit will be:
\[ F_{\text{new}} = 32 + 36 = 68 \text{ degrees Fahrenheit} \]

### Step 5: Calculate the corresponding Celsius temperature at the new Fahrenheit
Now, substitute \( F_{\text{new}} \) into the rearranged formula to find the new Celsius temperature:
\[ C_{\text{new}} = \frac{5}{9}(68 - 32) \]
\[ C_{\text{new}} = \frac{5}{9}(36) \]
\[ C_{\text{new}} = \frac{5 \times 36}{9} \]
\[ C_{\text{new}} = \frac{180}{9} = 20 \text{ degrees Celsius} \]

### Step 6: Determine the increase in Celsius
The increase in Celsius temperature is:
\[ \text{Increase in C} = C_{\text{new}} - C_{\text{initial}} \]
\[ \text{Increase in C} = 20 - 0 = 20 \text{ degrees} \]

### Final Answer
Thus, the corresponding increase in the Celsius scale when the temperature in Fahrenheit increases by 36 degrees is:
\[ \boxed{20 \text{ degrees}} \]

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