Question

If the moisture content of a sample on dry basis is 100%; the moisture content expressed on wet basis will be

• A. 25%
• B. 50%
• C. 75%
• D. 125%

Hint:

- When water mass equals dry matter mass, dry basis moisture is \( 100% \), and wet basis moisture is \( 50% \) (since water makes up half of the total mass).
- Wet basis moisture content can never exceed \( 100% \), while dry basis moisture content can exceed \( 100% \).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Moisture content in agricultural materials can be expressed on two different bases:
1. Wet Basis (\( M_w \)): The mass of water divided by the total mass of the sample (dry matter plus water).
2. Dry Basis (\( M_d \)): The mass of water divided by the mass of dry matter in the sample.
We can convert between these two bases using standard mathematical relationships.
Key Formula or Approach:
The formula to convert moisture content from dry basis (\( M_d \)) to wet basis (\( M_w \)) is:
\[ M_w = \frac{M_d}{1 + M_d} \times 100% \]
where \( M_d \) is expressed as a decimal.

Step 2: Detailed Explanation:
Let us perform the calculation step-by-step:
1. Identify the given value:
- Moisture content on a dry basis, \( M_d = 100% \).
- Convert the percentage to a decimal:
\[ M_d = \frac{100}{100} = 1.0 \]
This means the mass of water in the sample is exactly equal to the mass of dry matter.
2. Substitute \( M_d = 1.0 \) into the conversion formula:
\[ M_w = \frac{1.0}{1 + 1.0} \times 100% \]
3. Simplify the expression:
\[ M_w = \frac{1.0}{2.0} \times 100% \]
\[ M_w = 0.5 \times 100% = 50% \]
Therefore, a moisture content of \( 100% \) on a dry basis corresponds to \( 50% \) on a wet basis.

Step 3: Final Answer:
The moisture content expressed on a wet basis is 50%.