Question

Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R).
Assertion (A) : Moisture content of a fruit or a vegetable expressed on wet basis is always greater than the moisture content expressed on dry basis.
Reason (R) : Moisture on wet basis is expressed with reference to total weight of the sample instead of its dry matter content.
In light of the above statements, choose the correct answer from the options given below.

• A. Both (A) and (R) are true and (R) is the correct explanation of (A).
• B. Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.

Hint:

Remember that dry basis moisture content can exceed 100% (e.g., highly moist biological materials like fresh fruits can have dry basis moisture contents of 400% or more).
Conversely, wet basis moisture content can never exceed or even reach 100% for any real, physical sample.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Moisture content in agricultural products is expressed in two ways: wet basis (\(M_w\)) or dry basis (\(M_d\)). These are defined based on the reference mass used in the denominator.
Key Formula or Approach:
Let \(W_w\) be the mass of water and \(W_d\) be the mass of dry matter in a sample.
The moisture content on a wet basis is: \[ M_w = \frac{W_w}{W_w + W_d} \] The moisture content on a dry basis is: \[ M_d = \frac{W_w}{W_d} \]

Step 2: Detailed Explanation:
Let us analyze the assertion and reason statements using these definitions:

Assertion (A): Since the denominator for wet basis (\(W_w + W_d\), representing total weight) is always greater than or equal to the denominator for dry basis (\(W_d\), representing dry matter only), the fraction for wet basis must be less than or equal to the dry basis fraction: \[ M_w \le M_d \] For any real food sample containing moisture (\(W_w > 0\)), the wet basis moisture content is always strictlyless than the dry basis moisture content.
For example, if a fruit has equal parts water and dry matter (\(W_w = 1\text{ kg}\), \(W_d = 1\text{ kg}\)): \[ M_w = \frac{1}{1+1} = 50\% \] \[ M_d = \frac{1}{1} = 100\% \] Here, the dry basis value is twice the wet basis value. Thus, Assertion (A) isfalse.

Reason (R): Wet basis moisture content is calculated relative to the total weight of the sample (wet weight), while dry basis moisture content is calculated relative to the dry matter content. Thus, Reason (R) istrue.
Therefore, Assertion (A) is false but Reason (R) is true.

Step 3: Final Answer:
The correct option is (D).