# GATE (TF) Textile 2004 Question Paper Solution | GATE/2004/TF/58

###### Question 58 (Textile Engineering & Fibre Science)

A blow room has three cleaners in series. The overall cleaning efficiency of the blow room is 60%. If the cleaning efficiencies of the first and the third cleaners are 30% and 25% respectively, the cleaning efficiency of the second cleaner is

Option D is correct.

Here, total blow room machine=3

Overall cleaning efficiency of the blow room=60%

Efficiency of first machine=30%

Efficiency of third machine=25%

Efficiency of the second machine=?

Let,
Feed trash in first machine=x1

Delivered trash of first machine or feed of 2nd machine=x2

Delivered trash of 2nd machine or feed trash of3rd machine=x3

Delivered trash of 3rd machine=x4

Efficiency of first machine=

=0.70 …………………………………………(1)

Smilarily-

Efficiency of third machine=25%

Efficiency of third machine=

25=

=0.75……………………………………………(2)

Overall cleaning efficiency of the blow room=60%

Overall cleaning efficiency of the blow room=

60=\frac{(x_1-x_4)}{x_1} \times 100\frac{x_4}{x_1}\frac{x_1}{x_4}=\frac{1}{0.40}\frac{x_2}{x_1} \times \frac{x_4}{x_3} \times \frac{x_1}{x_4}=0.70 \times 0.75 \times \frac{1}{0.40}\frac{x_2}{x_3}=1.311-\frac{x_2}{x_3}=0.30\$

Efficiency of the second machine=30%