# GATE (TF) Textile 2016 Question Paper Solution | GATE/2016/TF/36

###### Question 36 (Textile Engineering & Fibre Science)

If 50 bales of 5 µg/inch, 20 bales of 3.5 µg/inch and 40 bales of 3.0 µg/inch cotton fibres are mixed, the resultant µg/inch of the mixed cotton is __3.70 : 3.85__.

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Given in the question
Fineness of 50 bales=5 g/inch

Fineness of 20 bales=3.5 g/inch

Fineness of 40 bales=3.0 g/inch

Let us assume bales as grams
By unitary rule:
1) 50 bales of 5 g/inch

W1=50 g
1 inch length contained=5 g weight

i.e , 5 g weight have=1 inch length

1 g weight have=1/5

Then,

50 g weight have=50/5 inch length
L1 =10 inch

2) 20 bales of 3.5 g/inch

W2=20 g

1 inch length contained=3.5 g weight

i.e , 3.5 g weight have=1 inch length

1 g weight have=1/3.5

Then,

20 g weight have=20/3.5 inch length
L2 =5.71 inch

3) 40 bales of 3.0 g/inch

W2=40 g

1 inch length contained=3.0 g weight

i.e , 3.0 g weight have=1 inch length

1 g weight have=1/3.0

Then,

40 g weight have=40/3.0 inch length
L2 =13.33 inch

Now,
Total weight(W)=W1+W2+W3
=50+20+40

Total weight(W)=110 Total length(L)=L1+L2+L3

=10+5.71+13.33

Total length(L)=29.04 inch

Hence, 29.04 inch length have=110 g

1 inch length have=110/29.04

=3.79

Resultant g/inch=3.79 (Answer)