Question

Two yarns of count X each are doubled and plied. The ratio of resultant count of two ply yarn expressed in tex system and Ne system is_______. Neglect contraction due to twist.

• A. 4
• B. 2
• C. 1/2
• D. 1/4

Hint:

Remember the inverse relationship between direct (tex) and indirect (Ne) count systems. Doubling increases the count in tex but decreases the count in Ne. The ratio of resultant counts will always be a power of 2 (or its reciprocal) when doubling/plying identical yarns and neglecting contraction.

Answer 1

The Correct Option is A

Step 1: Understanding Count Systems: Tex (Direct System): Yarn count is the mass per unit length (grams per 1000 meters). A higher tex number means a thicker yarn. 
Ne (Indirect System): Yarn count is the length per unit mass (number of hanks of 840 yards per pound). A higher Ne number means a finer yarn. 

Step 2: Doubling and Plying: When two yarns of count X are doubled, their combined linear density (in a direct system like tex) doubles. When two yarns are plied, they are twisted together. We are told to neglect contraction due to twist, so we assume the length remains the same. 

Step 3: Calculating Resultant Count: Tex (Direct System): If each single yarn has a count of X tex, then the doubled yarn has a count of 2X tex. Since we are neglecting contraction, the plied yarn also has a count of 2X tex. 
Ne (Indirect System): If each single yarn has a count of X Ne, the doubled yarn has half the count, or X/2 Ne. Since length per unit mass is halved. Since we are told that the count of each yarn is same, we have X/2 Ne. 

Step 4: Finding the Ratio: We want the ratio of the resultant count in tex to the resultant count in Ne: \[ \frac{\text{Resultant Count (Tex)}}{\text{Resultant Count (Ne)}} = \frac{2X}{X/2} = 2X \cdot \frac{2}{X} = 4 \]