A faulty thermometer reads freezing point and boiling point of water as `-5 ^(@)C` abd `95^(@)C` respectively . What is the correct value of temperature as it reads `60^(@)C` on faulty thermometer?

Options

A. `60^(@)C`
B. `65^(@)C`
C. `64^(@)C`
D. `62^(@)C`

Explanation

To solve the problem of determining the correct temperature when the faulty thermometer reads 60°C, we can use the concept of linear interpolation based on the given freezing and boiling points.

### Step-by-Step Solution:

1. **Identify the given values**:
- Faulty thermometer freezing point (LFP): \( -5°C \)
- Faulty thermometer boiling point (UPF): \( 95°C \)
- Faulty thermometer reading (T_faulty): \( 60°C \)

2. **Determine the correct temperature scale**:
- The correct freezing point (C_LFP) is \( 0°C \).
- The correct boiling point (C_UPF) is \( 100°C \).

3. **Set up the linear relationship**:
The relationship between the faulty thermometer reading and the correct temperature can be expressed as:
\[ \frac{T_{faulty} - LFP}{UPF - LFP} = \frac{T_{correct} - C_{LFP}}{C_{UPF} - C_{LFP}} \]
Plugging in the values we have:
\[ \frac{60 - (-5)}{95 - (-5)} = \frac{T_{correct} - 0}{100 - 0} \]

4. **Simplify the fractions**:
- The left side becomes:
\[ \frac{60 + 5}{95 + 5} = \frac{65}{100} \]
- The equation now looks like:
\[ \frac{65}{100} = \frac{T_{correct}}{100} \]

5. **Cross-multiply to solve for T_correct**:
\[ 65 \cdot 100 = T_{correct} \cdot 100 \]
Thus, \( T_{correct} = 65°C \).

6. **Conclusion**:
The correct temperature corresponding to a reading of 60°C on the faulty thermometer is \( 65°C \).

### Final Answer:
The correct value of temperature when the faulty thermometer reads \( 60°C \) is \( 65°C \).