gain in efficiency math problem

[paulpeter1313]

My friend is tackling a math problem at work for work with a friend and debating/butting heads and so he decided to throw it against other friends to get a larger viewpoint, I am horrible at math but I thought this site seemed like the place to go to pick a few brains.... can anyone give me an answer to this....

work received 2008 "5,284" 6.25 full time employees
work received 2009 "79,941" 7 full time employees

What is the gain in efficiency?

 

[wjm11]

work received 2008 "5,284" 6.25 full time employees
work received 2009 "79,941" 7 full time employees

What is the gain in efficiency?

First, consider the 2008 data. Set up a ratio to calculate how much work would have been received with 7 employees at the 2008 efficiency level:

(5280/6.25) = (x/7)
x = 7(5280/6.25) = 5913.6

Next, compare this answer with the 2009 data to calculate how many times more work was received:

79941/5913.6 = 13.52 times as much work was received in 2009.

One could say that the work force was 13.5 times more efficient in 2009 than in 2008.

Hope that helps.

 

[chrisr]

Gain in efficiency can be expressed in different ways.
If output is doubled, that may be classed as a 100% gain in efficiency, as it is the "gain" being quantified,
not the output level.
If output is trebled, that's a 200% gain in efficiency,
quadrupled corresponds to a 300% gain.

Assuming one employee worked only a quarter of the time that the other 6 did in 2008,
divide 5284 by 6.25 to get the output per employee in 2008,
divide 79941 by 7 for the 2009 level.

Get the difference, express it as a ratio or fraction,
subtract 1 and put 2 zeros at the end of it and call it the percent gain.