Raghav was measuring a piece of cloth of length 2.5 m but by mistake he measured its length as 255 cm. Find the change in percentage in measuring the length.

Options

A. `1.5%`
B. `2.5%`
C. `2%`
D. `1%`

Answer

To find the change in percentage in measuring the length of the cloth, we can follow these steps:

### Step-by-Step Solution

1. **Convert the Length from Meters to Centimeters**:
Raghav's correct measurement is 2.5 meters.
Since 1 meter = 100 centimeters, we convert 2.5 meters to centimeters:
\[ 2.5 \text{ m} = 2.5 \times 100 = 250 \text{ cm} \]

2. **Identify the Mistaken Measurement**:
Raghav mistakenly measured the length as 255 cm.

3. **Calculate the Change in Measurement**:
To find the change in measurement, we subtract the correct measurement from the mistaken measurement:
\[ \text{Change} = \text{Mistaken Measurement} - \text{Correct Measurement} = 255 \text{ cm} - 250 \text{ cm} = 5 \text{ cm} \]

4. **Calculate the Percentage Change**:
The percentage change can be calculated using the formula:
\[ \text{Percentage Change} = \left( \frac{\text{Change}}{\text{Correct Measurement}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Change} = \left( \frac{5 \text{ cm}}{250 \text{ cm}} \right) \times 100 \]

5. **Perform the Calculation**:
\[ \text{Percentage Change} = \left( \frac{5}{250} \right) \times 100 = 0.02 \times 100 = 2\% \]

### Final Answer:
The change in percentage in measuring the length is **2%**.