Question

The ratio of moisture content on wet basis to moisture content on dry basis for wheat grain is 4:5. The ratio of weight of dry matter to weight of water in the grain is

• A. 4:1
• B. 4:5
• C. 1:4
• D. 5:4

Hint:

Write wet basis and dry basis moisture content as fractions of the same water and dry matter, then divide one by the other.

Answer 1

The Correct Option is A

Step 1: Write the two moisture content definitions.
Moisture content on wet basis is \( M_{wb} = \dfrac{W}{W+D} \), where \(W\) is the weight of water and \(D\) is the weight of dry matter.
Moisture content on dry basis is \( M_{db} = \dfrac{W}{D} \).

Step 2: Form the given ratio.
The problem gives \( \dfrac{M_{wb}}{M_{db}} = \dfrac{4}{5} \).
Divide the two expressions: \( \dfrac{M_{wb}}{M_{db}} = \dfrac{W/(W+D)}{W/D} = \dfrac{D}{W+D} \).
So \( \dfrac{D}{W+D} = \dfrac{4}{5} \).

Step 3: Solve for the dry matter to water ratio.
Cross multiply: \( 5D = 4W + 4D \), which gives \( D = 4W \).
So \( \dfrac{D}{W} = \dfrac{4}{1} \).

Final Answer:
The weight of dry matter to weight of water works out to 4:1, so option (A) is correct. Options (B), (C) and (D) come from mixing up which ratio belongs to wet basis and which to dry basis. \[ \boxed{D:W = 4:1} \]