A piece of cloth measured with a metre stick, one cm short, is 100 metres stick, . Reckoning the metre stick as being right, the actual length of the cloth (in cm) is

Options

A. 3, 900
B. 9, 900
C. 8, 000
D. 6, 100

Answer

To solve the problem, we need to determine the actual length of the cloth in centimeters, given that a meter stick is measuring one centimeter short.

### Step-by-Step Solution:

1. **Understanding the Measurement Error**:
The problem states that the meter stick is one centimeter short. This means that when the meter stick shows 1 meter, the actual length being measured is 1 cm less than that.

- Therefore, when the meter stick measures 1 meter (100 cm), the actual length is:
\[ 100 \text{ cm} - 1 \text{ cm} = 99 \text{ cm} \]

2. **Calculating the Actual Length for 100 Meters**:
If the meter stick shows 100 meters, we need to find out how much cloth that actually corresponds to in centimeters. Since the meter stick is consistently measuring 1 cm short, we can apply the same logic to 100 meters.

- First, convert 100 meters to centimeters:
\[ 100 \text{ m} = 100 \times 100 \text{ cm} = 10000 \text{ cm} \]

3. **Adjusting for the Measurement Error**:
Since the meter stick is measuring 1 cm short for every meter, we need to calculate the actual length of the cloth when the meter stick shows 100 meters.

- The actual length of the cloth can be calculated as:
\[ \text{Actual Length} = 10000 \text{ cm} - (100 \text{ m} \times 1 \text{ cm}) \]
- Since 100 m corresponds to 100 cm short, we subtract 100 cm from the total:
\[ \text{Actual Length} = 10000 \text{ cm} - 100 \text{ cm} = 9900 \text{ cm} \]

4. **Final Answer**:
Thus, the actual length of the cloth is:
\[ \text{Actual Length} = 9900 \text{ cm} \]

### Summary:
The actual length of the cloth, when measured with a meter stick that is 1 cm short, is **9900 cm**.