# 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.**

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 â‡’ 20 Ã— (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 â‡’ 30 Ã— (6 men and 12 women) can do the same work in 1 day.
So, efficiency of 20 Ã— (10 men and 9 women) = efficiency of 30 Ã— (6 men and 12 women)

Or, 200 men + 180 women = 180 men + 360 women

Or, 20 men = 180 women â‡’ 1 man = 9 women
So, the total work = 20 Ã— (10 men and 9 women) = 20 Ã— (90 + 9) women = 99 Ã— 20 = 1980 units
Total number of persons employed = 1 man + 1 women = 10 women
So, the time taken =

Or, 200 men + 180 women = 180 men + 360 women

Or, 20 men = 180 women â‡’ 1 man = 9 women