# GATE (TF) Textile 2014 Question Paper Solution | GATE/2014/TF/37

###### Question 37 (Textile Engineering & Fibre Science)

The twist contraction factor of a filament yarn is 1.06. For producing 5 ton twisted yarn of 50 tex, the untwisted yarn length required, in km, accurate to the nearest integer, is …………….

Write Here

Given in the question

Twist contraction=1.06

Amount of twisted yarn to be produced=5 ton

Yarn count=50 tex

Untwisted yarn length in km=?

Calculation:
Weight of twisted yarn=5 ton
=5000 kg
=5000000 gm
=5*106 gm

Yarn count=50 tex

By definition of tex

1000 meter length have=50 gm weight
i.e.,
50 gm weight have=1000 meter length

1 gm weight have=1000/50

Then,
5*106 gm weight have=1000*5*106/50 meter length

=108 meter

Length of twisted yarn=108 meter

Formula:
Twist contraction=Untwisted length/twisted length

Twist contraction=1.06

1.06=Untwisted length/twisted length

1.06=Untwisted length/108

Untwisted length=1.06 x 108

Untwisted length=106000000 meter

Length of untwisted yarn=106000 km (Answer)