A faulty thermometer has its fixed point marked at `6^(@)` and `96^(@)`. What is the correct temperature on the Centrigrade scale when this themometer reads `87^(@)`

Options

A. `83^(@)C`
B. `93^(@)C`
C. `90^(@)C`
D. `85^(@)C`

Explanation

To solve the problem of finding the correct temperature on the Centigrade scale when a faulty thermometer reads 87°C, we can follow these steps:

### Step 1: Understand the fixed points of the faulty thermometer
The faulty thermometer has its fixed points marked at 6°C and 96°C. These points correspond to the temperatures of 0°C and 100°C on the Centigrade scale.

### Step 2: Set up the relationship between the faulty thermometer and the Centigrade scale
We know that the temperature on the Centigrade scale (Tc) can be calculated using the formula that relates the readings of the faulty thermometer (Tf) to the fixed points:
\[ Tc = \frac{100}{96 - 6} \times (Tf - 6) \]
This simplifies to:
\[ Tc = \frac{100}{90} \times (Tf - 6) \]

### Step 3: Substitute the reading of the faulty thermometer
Now, we substitute Tf = 87°C into the equation:
\[ Tc = \frac{100}{90} \times (87 - 6) \]

### Step 4: Calculate the value
First, calculate \(87 - 6\):
\[ 87 - 6 = 81 \]
Now substitute this back into the equation:
\[ Tc = \frac{100}{90} \times 81 \]
This can be simplified to:
\[ Tc = \frac{10}{9} \times 81 \]

### Step 5: Perform the multiplication
Now calculate:
\[ Tc = \frac{10 \times 81}{9} = \frac{810}{9} = 90 \]

### Final Answer
The correct temperature on the Centigrade scale when the faulty thermometer reads 87°C is:
\[ \boxed{90°C} \]

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