# GATE (TF) Textile 2017 Question Paper Solution | GATE/2017/TF/43

###### Question 43 (Textile Engineering & Fibre Science)

In a fabric, warp count is 25 tex, weft count is 32 tex, ends per cm is 25, picks per cm is 15, warp crimp is 6% and weft crimp is 8%. The areal density of the fabric, in g/m2, accurate to two decimal places is __117.00 to 119.00__.

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Given in the question-
Warp count=25 tex

i.e. gm/meter of warp=25/1000 (By definition of tex i.e. grams in 1000 meter length)

Weft count=32 tex

i.e. gm/meter of weft=32/1000

EPCM=25

i.e. Ends per meter(EPM)=2500

PPCM=15

i.e. Picks per meter(PPM)=1500

Warp crimp=6%

Weft crimp=8%

The areal density(g/m2)=?

Formula:

Areal density of the fabric(g/m2)=Weight of warp yarn+Weight of weft yarn

Areal density of the fabric(g/m2)=EPM x gm per meter of warp x (1+(crimp%/100))+PPM x gm per meter of weft x (1+(crimp%/100))

Areal density of the fabric(g/m2)=2500 x (25/1000) x (1+6/100)+1500 x (32/1000) x (1+8/100)

Areal density of the fabric(g/m2)=(2500 x 25/1000) x (1+0.06)+(1500 x 32/1000) x (1+0.08)

Areal density of the fabric(g/m2)=2500 x 25 x 1.06/1000+1500 x 32 x 1.08/1000

Areal density of the fabric(g/m2)=(2500 x 25 x 1.06+1500 x 32 x 1.08)/1000

Areal density of the fabric(g/m2)=(66250+51840)/1000

Areal density of the fabric(g/m2)=118090/1000

Areal density of the fabric(g/m2)=118.09 (Answer)