Question

A cotton fabric is to be dyed with 2 % shade (on the weight of fabric). If dye concentration is 0.4 g/L, then the material-to-liquor ratio is 1 : X. The value of X (in integer) is

Hint:

- The material-to-liquor ratio is essential for determining the correct dye concentration and the amount of liquor required for dyeing fabrics. - For 2% shade, use the amount of dye per unit weight of fabric and the given dye concentration to calculate the required liquor volume.

Answer 1

Correct Answer: 50

Let the weight of fabric be 1 unit. The dye concentration is given as 0.4 g/L, and the required shade is 2% (which means 2 grams of dye for every 100 grams of fabric). We can set up the equation based on the material-to-liquor ratio: \[ \text{Material-to-liquor ratio} = \frac{\text{Weight of fabric}}{\text{Volume of liquor}} = \frac{1}{X} \] Now, the amount of dye required for 2% shade is 2 grams for every 100 grams of fabric. To achieve this shade, we need: \[ \text{Dye concentration} \times \text{Volume of liquor} = \text{Amount of dye required}
0.4 \times X = 2 \] Solving for \( X \): \[ X = \frac{2}{0.4} = 5 \] Therefore, the material-to-liquor ratio is 1 : 50.