A centigrade and a Fehrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fehrenheit thermometer registers `140^(@)C` . What is the fall in temperature as register by the centigrade thermometer

Options

A. `30^(@)`
B. `40^(@)`
C. `60^(@)`
D. `80^(@)`

Explanation

To solve the problem, we need to determine the fall in temperature as registered by a centigrade thermometer when the Fahrenheit thermometer reads 140°F. Here’s a step-by-step solution:

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

### Step 2: Substitute the Fahrenheit value
We know that the Fahrenheit thermometer reads 140°F. We will substitute this value into the formula:
\[ C = \frac{5}{9} (140 - 32) \]

### Step 3: Calculate the Celsius temperature
Now, we simplify the equation:
1. Calculate \(140 - 32\):
\[ 140 - 32 = 108 \]
2. Now substitute this back into the equation:
\[ C = \frac{5}{9} \times 108 \]
3. Calculate \( \frac{5}{9} \times 108 \):
\[ C = 60 \]

### Step 4: Determine the fall in temperature
The boiling point of water is 100°C. To find the fall in temperature, we subtract the Celsius reading from the boiling point:
\[ \text{Fall in temperature} = 100°C - 60°C = 40°C \]

### Final Answer
The fall in temperature as registered by the centigrade thermometer is **40°C**.

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