GATE (TF) Textile 2005 Question Paper Solution | GATE/2005/TF/36

On examination of 200 cotton fibres, 120 normal, 60 semi mature and 20 dead fibres are observed. Maturity ratio of this cotton is

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Option D is correct.

Given-

Total no. of fibres=200

Normal fibres=120

Semi mature fibres=60

Dead fibres=20

Maturity ratio(M.R.)=?

By formula-

$M.R.=\frac{N-D}{100}+0.725$

This formula is for total 100 fibres
Here,

200 total fibres have……………….=120 normal fibres

Then, 100 total fibres have…….=120 x 100/200

Normal fibes(N)=60

Similarily,

200 total fibres have……………….=60 semi mature fibres

Then, 100 total fibres have…….=60 x 100/200

Semi mature fibres(S)=30

And

200 total fibres have……………….=20 dead fibres

Then, 100 total fibres have…….=20 x 100/200

Dead fibres(S)=10

Now, put these values in to the formula-

$M.R.=\frac{60-10}{100}+0.725$

$M.R.=\frac{50}{100}+0.725$

M.R.=1.22 (Ans)