GATE (TF) Textile 2008 Question Paper Solution | GATE/2008/TF/85

Statements Linked Answer Questions

100 fibres were tested for maturity. The normal (N) and thin walled (T) fibres were found to be 60 and 20 respectively

Question 85 (Textile Engineering & Fibre Science)

If the number of matured fibres increases by 10% with number of thin walled fibres remaining the same, the percent increase in maturity ratio would be

(A)	5.6
(B)	6.6
(C)	8.3
(D)	10

[Show Answer]

Option B is correct.
Given in the question-

Normal fibre( $N_1$ )=60

Normal fibre( $N_2$ )=60+60 x 10%

Normal fibre( $N_2$ )=60+6

Normal fibre( $N_2$ )=66

Thin walled fibre(T)=20

The maturity ratio=?

Here, we aasume 100 total number of fibres

Then , Dead fibres(D1)=100-N-T

D1=100-60-20

D1=20

By formula-

$Maturity ratio_1=\frac{N_1-D_1}{200}+0.7$

$Maturity ratio_1=\frac{60-20}{200}+0.7$

$Maturity ratio_1=\frac{40}{200}+0.7$

$Maturity ratio_`=0.2+0.7$

Maturity ratio1(M.R1)=0.9

And

Dead fibres(D2)=100-N2-T

Dead fibres(D2)=100-66-20

Dead fibres(D2)=14

$Maturity ratio_2=\frac{N_2-D_2}{200}+0.7$

$Maturity ratio_2=\frac{66-14}{200}+0.7$

$Maturity ratio_2=\frac{52}{200}+0.7$

$Maturity ratio_2=0.26+0.7$

Maturity ratio2(M.R.2)=0.96

Now,

The percent increase in maturity ratio=(M.R.2-M.R.1) x 100/M.R. 1

The percent increase in maturity ratio=(0.96-0.9) x 100/0.9

The percent increase in maturity ratio=0.06 x 100/0.9

The percent increase in maturity ratio=6.66 (Ans)

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