# GATE (TF) Textile 2013 Question Paper Solution | GATE/2013/TF/44

###### Question 44 (Textile Engineering & Fibre Science)

In the case of reactive dyeing of cotton, the exhaustion is 70% and reaction efficiency is 80%. Assuming that the initial dye concentration is 2% on the weight of fabrics, the amount of unreacted dye on the fabric expressed as a percentage of fabric weight would be

Exhaustion =70%

Reaction efficiency=80%

Initial dye concentration=2%

Amount of unreacted dye on fabric expressed as a percentage of fabric=?

Calculation

Let the fabric weight =100 kg

Weight of dye=100 x 2/100

Weight of dye=2 kg

Dye exhausted=2 x 70/100

Dye exhausted=1.4 kg

Dye reacted=1.4 x 80/100

Dye reacted=1.12 kg

Amount of unreacted dye=Exhausted dye-Reacted dye

Amount of unreacted dye=1.4-1.12

Amount of unreacted dye=0.28 kg

The amount of unreacted dye on the fabric expressed as a percentage of fabric weight=(Amount of unreacted dye/Weigh of fabric)*100

The amount of unreacted dye on the fabric expressed as a percentage of fabric weight=0.28*100/100

The amount of unreacted dye on the fabric expressed as a percentage of fabric weight=0.28 (Answer)

Hence option B is correct