Question

Calculate the count of the two fold cotton yarn composed of 24s and 40s singles.

• A. \( 15\text{s} \)
• B. \( 30\text{s} \)
• C. \( 60\text{s} \)
• D. \( 10\text{s} \)

Hint:

In direct systems like Denier or Tex, you simply add the counts ($n_1 + n_2$). In indirect systems like Cotton Count, you must always use the "Product over Sum" formula.

Answer 1

The Correct Option is A

Concept: The English Cotton Count (Ne) is an indirect yarn numbering system. In this system, the count represents the number of hanks (840 yards) that weigh one pound. This means a higher number indicates a finer (thinner) yarn. When two yarns are folded or twisted together, the resulting yarn is thicker, and therefore its "resultant count" will be a smaller number.

Step 1: Apply the formula for resultant count in an indirect system.
When twisting two different single yarns ($n_1$ and $n_2$), the resultant count ($N$) is calculated using the following harmonic mean formula: \[ \frac{1}{N} = \frac{1}{n_1} + \frac{1}{n_2} \quad \text{or} \quad N = \frac{n_1 \times n_2}{n_1 + n_2} \]

Step 2: Plug in the given values.
Substituting $n_1 = 24$ and $n_2 = 40$: \[ N = \frac{24 \times 40}{24 + 40} \] \[ N = \frac{960}{64} \] \[ N = 15 \]

Step 3: Interpret the result.
The two-fold yarn has a count of 15s. It is logically consistent that the resulting yarn (15s) is thicker than both the 24s and 40s individual singles used to create it.