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
| (A) | 5.0% |
| (B) | 11.9% |
| (C) | 22.4% |
| (D) | 23.8% |
[Show Answer]
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%