# GATE (TF) Textile 2010 Question Paper Solution | GATE/2010/TF/38

###### Question 38 (Textile Engineering & Fibre Science)

100 kg of 67/33 polyester/cotton blended yarn with 4% moisture content is shipped. The standard moisture regain values of polyester and cotton are 0.4% and 8.5% respectively. The correct invoice weight is approximately

Given in the question-

Weight of 67/33 polyester/cotton blended yarn=100 kg

Moisture content of blended yarn=4%

Moisture regain value of polyester yarn=0.4%

Moisture regain value of cotton yarn=8.5%

The correct invoice weight(W+D)=?

Where,
D=Oven dry weight of blend yarn

W=Weight of water present

Blend yarn weight=Oven dry weight of blend yarn+Oven dry weight of blend yarn x Moisture content%

100=D+D x 4/100

100=D+D x 0.04

100=1.04 D

D=100/1.04

Oven dry weight of yarn(D)=96.15 kg

Now,

Moisutre regain of blend yarn(M.R)=Weight % of polyester x Moisture regain value of polyester yarn+Weight % of cotton x Moisture regain value of cotton yarn/(Weight % of polyester+Weight % of cotton)

Moisutre regain of blend yarn(M.R)=67 x 0.4%+33 x 8.5% / (67+33)

Moisutre regain of blend yarn(M.R)=67 x 0.4%+33 x 8.5% / (67+33)

Moisutre regain of blend yarn(M.R)=0.268+2.805/ (100)

Moisutre regain of blend yarn(M.R)=3.073/ 100

Moisutre regain of blend yarn(M.R%)=(3.073/ 100) x 100

Moisutre regain of blend yarn(M.R%)=3.073 %

By formula-

Moisture regain%=W x 100/D

3.073=W x 100/96.15

W=3.073 x 96.15/100

W=295.47/100

W=2.95 kg

Now,

The correct invoice weight=(W+D)

=96.15+2.95

The correct invoice weight=99.10 kg (Ans)