# GATE (TF) Textile 2008 Question Paper Solution | GATE/2008/TF/40

###### Question 40 (Textile Engineering & Fibre Science)

Cleaning efficiency (%) of blow room having four machines is 39.6. If the cleaning efficiencies of the first, second and fourth (last) machines are 10, 20 and 20 respectively, then than of the third machine is

Given in the question-

Cleaning efficiency(%) of blow room(have 4 m/c)=39.6

Cleaning efficiency of first machine=10

Cleaning efficiency of second machine=20

Cleaning efficiency of fourth machine=20

Cleaning efficiency of third machine=?

Let,

Trash in 1st machine=T1

Trash in 2nd machine=T2

Trash in 3rd machine=T3

Trash in 4 th machine=T4

By formula-

Cleaning efficiency(%) of blow room(have 4 m/c)=(Trash in 1st machine-Trash in 4 th machine) x 100/Trash in 1st machine

39.6=(T1-T4) x 100/T1

0.396=1-T4/T1

T4/T1=1-0.396

T4/T1=0.604

And

Cleaning efficiency of first machine=(Trash in 1st machine-Trash in 2nd machine) x 100/Trash in 1st machine

10=(T1-T2) x100/T1

0.1=1-T2/T1

T2/T1=1-0.1

T2/T1=0.9

Similarily-

Cleaning efficiency of 2nd machine=(Trash in 2nd machine-Trash in 3rd machine) x 100/Trash in 2nd machine

T3/T2=0.8

And

T4/T1 x T1/T2 x T2/T3=0.604 x (1/ 0.9) x (1/0.8)

T4/T3=0.84

1-T4/T3=1-0.84

1-T4/T3=0.16

Cleaning efficiency of 3rd machine=(Trash in 3rd machine-Trash in 4th machine) x 100/Trash in 3rd machine

Cleaning efficiency of 3rd machine=(T3-T4) x100 /T3

Cleaning efficiency of 3rd machine=(1-T4/T3) x100

Cleaning efficiency of 3rd machine=0.16 x 100

Cleaning efficiency of 3rd machine=16% (Ans)