A faulty thermometer reads `5^@ C` melting ice and `99^@ C` in steam. Find the correct temperature in .^(@) F` when this faulty thermometer reads `52^@ C`.

Explanation

To solve the problem step-by-step, we need to find the correct temperature in Fahrenheit when the faulty thermometer reads 52°C.

### Step 1: Understand the Faulty Thermometer Scale
The faulty thermometer reads:
- 5°C for the melting ice (0°C)
- 99°C for steam (100°C)

### Step 2: Establish the Conversion Formula
We can set up a proportion based on the readings of the faulty thermometer and the actual Celsius scale:
- Let \( T_S \) be the reading on the faulty thermometer.
- Let \( T_C \) be the actual temperature in Celsius.

The relationship can be expressed as:
\[ \frac{T_S - 5}{99 - 5} = \frac{T_C - 0}{100 - 0} \]
This simplifies to:
\[ \frac{T_S - 5}{94} = \frac{T_C}{100} \]

### Step 3: Substitute the Faulty Reading
Now, we substitute \( T_S = 52 \) into the equation:
\[ \frac{52 - 5}{94} = \frac{T_C}{100} \]
This simplifies to:
\[ \frac{47}{94} = \frac{T_C}{100} \]

### Step 4: Solve for \( T_C \)
Cross-multiplying gives:
\[ 47 \times 100 = 94 \times T_C \]
\[ 4700 = 94 T_C \]
Now, divide both sides by 94:
\[ T_C = \frac{4700}{94} \approx 50°C \]

### Step 5: Convert Celsius to Fahrenheit
Now that we have the correct temperature in Celsius, we can convert it to Fahrenheit using the formula:
\[ T_F = \frac{9}{5} T_C + 32 \]
Substituting \( T_C = 50 \):
\[ T_F = \frac{9}{5} \times 50 + 32 \]
Calculating this gives:
\[ T_F = 90 + 32 = 122°F \]

### Final Answer
The correct temperature when the faulty thermometer reads 52°C is **122°F**.