Thermometer A and B have ice points marked at `15^@` and `25^@` and steam points at `75^@` and J `25^@` respecti vely. When thermometer A measures the temperature of a bath as `60^@`, the reading ofB for the same bath is

Options

A. `60^@`
B. `75^@`
C. `90^@`
D. `100^@`

Explanation

To solve the problem, we will use the relationship between the readings of two thermometers based on their ice and steam points. The formula we will use is:

\[ \frac{C}{100} = \frac{X - Z}{Y - Z} \]

Where:
- \( C \) is the temperature in degrees Celsius,
- \( X \) is the reading on the thermometer,
- \( Z \) is the ice point of the thermometer,
- \( Y \) is the steam point of the thermometer.

### Step-by-Step Solution:

1. **Identify the Ice and Steam Points for Thermometer A:**
- Ice point (ZA) = 15°C
- Steam point (YA) = 75°C

2. **Identify the Reading on Thermometer A:**
- Reading on thermometer A (A) = 60°C

3. **Set Up the Equation for Thermometer A:**
- Using the formula, we can write:
\[ \frac{C_A}{100} = \frac{A - Z_A}{Y_A - Z_A} \]
Substituting the known values:
\[ \frac{C_A}{100} = \frac{60 - 15}{75 - 15} \]
Simplifying the right side:
\[ \frac{C_A}{100} = \frac{45}{60} \]
Further simplifying gives:
\[ \frac{C_A}{100} = \frac{3}{4} \]
Therefore:
\[ C_A = 75°C \]

4. **Identify the Ice and Steam Points for Thermometer B:**
- Ice point (ZB) = 25°C
- Steam point (YB) = 125°C

5. **Set Up the Equation for Thermometer B:**
- We need to find the reading on thermometer B (B):
\[ \frac{C_B}{100} = \frac{B - Z_B}{Y_B - Z_B} \]
Substituting the known values:
\[ \frac{75}{100} = \frac{B - 25}{125 - 25} \]
Simplifying the right side:
\[ \frac{75}{100} = \frac{B - 25}{100} \]

6. **Cross-Multiply to Solve for B:**
\[ 75 \times 100 = 100 \times (B - 25) \]
\[ 7500 = 100B - 2500 \]
Adding 2500 to both sides:
\[ 100B = 10000 \]
Dividing by 100:
\[ B = 100°C \]

### Final Answer:
The reading of thermometer B for the same bath is **100°C**.