# GATE (TF) Textile 2018 Question Paper Solution | GATE/2018/TF/46

###### Question 46 (Textile Technology & Fibre Science)

A sliver of 4.2 kilotex is fed in a rotor spinning machine with opening zone draft of 1400. The draft in the transport duct is 5 and the sliding draft on the rotor wall till the rotor groove is 2. If the total back doubling within the rotor is 120, then the linear density (in tex) of the output yarn is __35.0 to 38.0__.

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Given in the question

Linear density of feed sliver=4.2 kilotex

Opening zone draft=1400

Draft in the transport duct=5

Sliding draft on the rotor wall till the rotor groove=2

Total back doubling=120

Linear density of the output yarn=?

Calculation

Total draft=opening zone draft*draft in transport duct*Sliding draft on rotor wall till rotor groove/Total back doubling

Total draft=1400*5*2/120

Total draft=117

Now,
Total draft=Linear density of input sliver/Linear density of output sliver

117=4.2/Linear density of output sliver

Linear density of output sliver=4.2/117

Linear density of output sliver=0.0359 kilotex

Linear density of output sliver=0.0359*1000

Linear density of output sliver=35.90 tex (Answer)