Question

In a factory, there are 100 skilled, 250 semi-skilled & 150 unskilled workers. It is observed

that on an average a unit is produced by a skilled worker in 3 hours, by a semiskilled worker

in 4 hours and by an unskilled worker in 5 hours. After a training of 3 years, the semi-skilled

workers became skilled & the unskilled workers became semi-skilled. How much less time

will be required after 3 years of training for producing a unit by an average worker? find answer in numerical
​

Answer 1

Given : In a factory, there are 100 skilled, 250 semi-skilled & 150 unskilled workers

on an average a unit is produced by a skilled worker in 3 hours

by a semiskilled worker   in 4 hours

by an unskilled worker in 5 hours

To Find :  How much less time  will be required after 3 years of training for producing a unit by an average worke

Solution:

100 skilled,

250 semi-skilled &

150 unskilled workers.

a unit is produced by a skilled worker in 3 hours

=> 100/3  units in 1 hr  by 100 skilled, worker

semiskilled worker  in 4 hours

=>  250/4  units in 1 hr  by 250 semi-skilled

unskilled worker in 5 hours

=> 150/5  units in 1 hr  by 150 unskilled workers

Total units in 1 hr  =  100/3 + 250/4  +  150/5

= 100/3 + 125/2 + 30

= (200 + 375 + 180)/6

= 755/6  units in 1 hr by (100 + 250 + 150 = 500 workers)

= 755/3000  units by 1  worker in 1 hr

=> Time required  for 1 unit on average by 1 worker = 3000/755  hr

= 3.97  hr

After Training

100+250 = 350  skilled,

150 semi-skilled  

350/3  units in 1 hr  by 350 skilled, worker

=>  150/4  units in 1 hr  by 150 semi-skilled

350/3 + 150/4

= (700 + 225)/6

= 925/6

= 925/3000  units by 1  worker in 1 hr

Time required  = 3000/925  hr = 3.24  hr

Time saved = 3000/755 -  3000/925

=  600/151 - 600/185

= 600 (34)/(151 * 185)

= 0.73   hr

less time  required after 3 years of training for producing a unit by an average worker = 0.73 hr

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