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Collective Work and Collective Efficiency

When people of different efficiencies start working together, the method of time-work equivalence to find the time or the amount of work done cannot be used. In those cases, we will be required to relate time with the efficiency of a group.
 
For example, if 5 men and 8 women can do a piece of work in 10 days, from this information we can not find out that in how many days a man or a woman can do the work individually, since we are not aware of their individual efficiencies. However, if we get a similar equation like x men and y women can do the same work in ‘p’ days, then we can correlate these two equations to find the number of days taken by one man and one woman to do the work.
 
Example
10 men and 9 women can do a piece of work in 20 days. The same work can be done by 6 men and 12 women in 30 days. In how many days can the same work be done by 1 man and 1 woman?
Solution
10 men and 9 women can do a work in 20 days ⇒ 20 × (10 men and 9 women) can do the same work in 1 day.
 
Similarly, 6 men and 9 women can do the same work in 30 days ⇒ 30 × (6 men and 12 women) can do the same work in 1 day.
 
So, efficiency of 20 × (10 men and 9 women) = efficiency of 30 × (6 men and 12 women)
Or, 200 men + 180 women = 180 men + 360 women
Or, 20 men = 180 women ⇒ 1 man = 9 women
 
So, the total work = 20 × (10 men and 9 women) = 20 × (90 + 9) women = 99 × 20 = 1980 units
 
Total number of persons employed = 1 man + 1 women = 10 women
 
So, the time taken = Description: 2309.png
 





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