# GATE (TF) Textile 2013 Question Paper Solution | GATE/2013/TF/40

###### Question 40 (Textile Engineering & Fibre Science)

The daily production of a mill is 1200 kg of 30 tex and 1200 kg of 20 tex yarns. The average yarn tex produced by the mill is

1)Production(P1)=1200 kg
=1200000 gm

Tex(T1)=30
i.e., 30 gm weight of yarn have=1000 meter length

1 gm weight yarn will have=1000/30

Then, 1200000 gm weight have=1000*1200000/30

Length of 30 tex yarn by production P1=40000000 meter
Length(L1)=4*107 meter

2)Production(P2)=1200 kg
=1200000 gm

Tex(T2)=20
i.e., 20 gm weight yarn have=1000 meter length

so, 1 gm will have……=1000/20

Then, 1200000 gm weight will have=1000*1200000/20
=60000000 meter length

Length of 20 tex yarn by production P2=6*107

Length(L2)=6*107 meter

Total length produced(L)=L1+L2

L=4*107+6*107

L=10*107 meter
and
Tota l production(P)=P1+P2
P=1200000+1200000

P=2400000 gm

Now,we have calculated
Total length(L)=10*107 meter
L=108 meter

Total weight(P)=2400000 gm
P=24*105

By definition of tex

108 meter total yarn length have=24*105 gm total weight

1 meter yarn length have=24*105/108

Then, 1000 meter yarn length have=24*105 x 1000/108

=24

i.e , Tex=24

i.e., The average yarn tex produced by the mill is 24 (Answer)