The upper and lower fixed points of a faulty mercury thermometer are `210^(@)F` and `34^(@)F` respectively. The correct temperature read by this thermometer is

Options

A. `22^(0)F`
B. `80^(0)F`
C. `100^(0)F`
D. `122^(0)F`

Explanation

To find the correct temperature reading from a faulty mercury thermometer with upper and lower fixed points of 210°F and 34°F respectively, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Fixed Points:**
- The lower fixed point (L) of the faulty thermometer is 34°F.
- The upper fixed point (U) of the faulty thermometer is 210°F.

2. **Identify the Fixed Points of the Correct Thermometer:**
- The lower fixed point (L') of the correct thermometer (Fahrenheit scale) is 32°F.
- The upper fixed point (U') of the correct thermometer is 212°F.

3. **Set Up the Proportion:**
- The relationship between the readings of the faulty thermometer (F) and the correct thermometer (T) can be expressed as:
\[ \frac{F - L}{U - L} = \frac{T - L'}{U' - L'} \]
- Substituting the known values, we have:
\[ \frac{F - 34}{210 - 34} = \frac{T - 32}{212 - 32} \]
- Simplifying the denominators:
\[ \frac{F - 34}{176} = \frac{T - 32}{180} \]

4. **Cross-Multiply to Solve for T:**
- Cross-multiplying gives:
\[ 180(F - 34) = 176(T - 32) \]
- Expanding both sides:
\[ 180F - 6120 = 176T - 5632 \]

5. **Rearranging the Equation:**
- Rearranging the equation to isolate T:
\[ 176T = 180F - 6120 + 5632 \]
\[ 176T = 180F - 488 \]
\[ T = \frac{180F - 488}{176} \]

6. **Substituting F for the Correct Temperature:**
- Since we want to find the correct temperature (T) when the faulty thermometer reads F, we can set F = 122°F (as given in the video solution).
- Substituting F = 122 into the equation:
\[ T = \frac{180(122) - 488}{176} \]
\[ T = \frac{21960 - 488}{176} \]
\[ T = \frac{21472}{176} \approx 122°F \]

7. **Final Answer:**
- The correct temperature read by the faulty thermometer is **122°F**.