Question

In a ring bobbin, the actual yarn weight is 75 grams with count 30 tex, calculate the length of the yarn in meters.

• A. 7500 meters
• B. 250 meters
• C. 25 meters
• D. 2500 meters

Hint:

The formula connecting Tex, weight, and length is: \[ \text{Length (m)} = \frac{\text{Weight (g)} \times 1000}{\text{Tex}} \] Plugging in the values: \( \text{Length} = \frac{75 \times 1000}{30} = 2500 \) meters.

Answer 1

The Correct Option is D

Step 1: Understand the definition of the Tex count system. A count of 30 tex means that 1000 meters of this yarn weigh 30 grams.
\[ 30 \, \text{tex} = \frac{30 \, \text{grams}}{1000 \, \text{meters}} \]

Step 2: Set up the problem. We know the total weight of the yarn on the bobbin is 75 grams, and we know the weight per 1000 meters. We need to find the total length.
We can write the relationship as: \[ \text{Length (m)} = \frac{\text{Total Weight (g)}}{\text{Weight per meter (g/m)}} \] First, find the weight per meter: \[ \text{Weight per meter} = \frac{30 \, \text{g}}{1000 \, \text{m}} = 0.03 \, \text{g/m} \]

Step 3: Calculate the total length.
\[ \text{Length (m)} = \frac{75 \, \text{g}}{0.03 \, \text{g/m}} = \frac{75}{3/100} = 75 \times \frac{100}{3} = 25 \times 100 = 2500 \, \text{meters} \] Alternative Method (using proportion): If 30 grams correspond to 1000 meters, Then 75 grams correspond to X meters. \[ \frac{1000 \, \text{m}}{30 \, \text{g}} = \frac{X \, \text{m}}{75 \, \text{g}} \] \[ X = \frac{1000 \times 75}{30} = \frac{75000}{30} = \frac{7500}{3} = 2500 \, \text{meters} \]