The freezing point on a thermometer is marked as `20(0)` and the boliling point as `150^(@)`. A temperature of `60^(@)C` on this thermomemter will be read as

Options

A. `40^(@)`
B. `65^(@)`
C. `98^(@)`
D. `110^(@)`

Explanation

To solve the problem, we need to determine how the temperature of 60°C corresponds to the readings on the given thermometer, which has its freezing point at 20°C and boiling point at 150°C.

### Step-by-Step Solution:

1. **Identify the known values**:
- Freezing point on the thermometer (T_f) = 20°C
- Boiling point on the thermometer (T_b) = 150°C
- Temperature to convert (T_C) = 60°C

2. **Determine the range of the thermometer**:
- The range of the thermometer is from the freezing point to the boiling point:
\[ T_b - T_f = 150°C - 20°C = 130°C \]

3. **Set up the proportion**:
- We can set up a proportion based on the temperature difference:
\[ \frac{T_C - T_f}{T_b - T_f} = \frac{X - T_f}{T_b - T_f} \]
- Here, \(X\) is the reading on the thermometer that we need to find.

4. **Substituting the known values**:
- Substitute the known values into the proportion:
\[ \frac{60°C - 20°C}{130°C} = \frac{X - 20°C}{130°C} \]
- This simplifies to:
\[ \frac{40°C}{130°C} = \frac{X - 20°C}{130°C} \]

5. **Cross-multiply to solve for X**:
- Cross-multiplying gives:
\[ 40°C \cdot 130°C = (X - 20°C) \cdot 130°C \]
- Simplifying this gives:
\[ 40 = X - 20 \]

6. **Solve for X**:
- Rearranging the equation:
\[ X = 40 + 20 = 60 \]

7. **Final step**:
- Now we need to convert the temperature reading:
\[ X = 20 + \left(\frac{130}{100} \times 60\right) \]
- Calculating this gives:
\[ X = 20 + 78 = 98°C \]

Thus, the reading on the thermometer for a temperature of 60°C will be **98°C**.