###### Question 47 (Textile Engineering & Fibre Science)

In a flat yarn, the number of filaments in the yarn cross section is 271. The yarn is divide into 5 segment of equal radial increments which are numbered as 1, 2, 3, 4 and 5, from yarn core to surface respectively. The approximately number of fibres in the 4^{th} segment is

(A) | 50 |

(B) | 80 |

(C) | 90 |

(D) | 110 |

**[Show Answer]**

Option B is correct.

Total number of filament in the yarn cross section=271

Let us assume,

The radius of 5th segment=5x

Then, area of 5th segment will be=

Area up to 5th segment=

Now, Area of 4 the segment=Area up to 4 th segment-Area up to 3 rd segment.

Area of 4 the segment=

Area of 4 the segment=

Area of 4 the segment=

By unitary rule-

Up to 5th segment area has………………………………………………=271 total no. of filament

Area has……………………………….=271 filament

4th segment area( filament

Total number of filaments in 4 th segment=75.88

Total number of filaments in 4 th segment(Aprroximately)=80 (Ans)