I am a software engineer. We are creating an efficiency report of employees.
we have two reports detail and summary of efficiency of employees.

while calculating detail report we are picking up each jobcard done by an employee . Following is the example
formula applied is as follows
-------------------------------------------------------------------------
Time units *.60 * Punched minutes for the month / Total Punched minutes
--------------------------------------------------------------------------

jobcard nr.| TU |Total punched minutes | Punched minutes for the month| = sold minutes
JC/134638 400*.60 1004 801 = 191
(400*.60*801/1004)
JC/135933 150*.60 117 117 = 90
(150*.6*117/117) ----
(281)

while calculating summary report we are picking up sum of jobcards for each employee. So the above said formula is used on the sum of each component of formula. Example is as follows
400 1004 801
150 117 117
---- ---- ----
550 1121 918
(550*.60*918/1121) =(270)

Can Any one please explain me why this difference is coming of 11 minutes
Between 281 and 270 in spite of using the same formula?

You are calculating something like this:
(a_i)*(b_i)*(c_i)/(d_i)
a_i means it's a number we'll call "a" and give it index "i"

So, if you have 2 such sets of numbers, you want to add them together. Let's look at the way you do it.

You say that a_1 * b_1 * c_1 / d_1 + a_2 * b_2 * c_2 / d_2 = (a_1 + a_2) * (b_1 + b_2) * (c_1 + c_2) / (d_1 + d_2)
That is, however, untrue. Problem is in dividing by d_i.

Correct formula would be:
a_1 * b_1 * c_1 / d_1 + a_2 * b_2 * c_2 / d_2 = ( a_1 * b_1 * c_1 * d_2 + a_2 * b_2 * c_2 * d_1 ) / (d_1*d_2)
Let's try it on your numbers.

(400*.6*801/1004) + (150*.6*117/117) = 191,47 + 90 = 281,47

(400*.6*801*117 + 150*.6*117*1004) / (1004*117) = (22492080 + 10572120) / 117468 = 33064200 / 117468 = 281,47

Thanks a lot . I appreciate this. I shall definitely try this on our program. Thanks from our team.


You are calculating something like this:
(a_i)*(b_i)*(c_i)/(d_i)
a_i means it's a number we'll call "a" and give it index "i"

So, if you have 2 such sets of numbers, you want to add them together. Let's look at the way you do it.

You say that a_1 * b_1 * c_1 / d_1 + a_2 * b_2 * c_2 / d_2 = (a_1 + a_2) * (b_1 + b_2) * (c_1 + c_2) / (d_1 + d_2)
That is, however, untrue. Problem is in dividing by d_i.

Correct formula would be:
a_1 * b_1 * c_1 / d_1 + a_2 * b_2 * c_2 / d_2 = ( a_1 * b_1 * c_1 * d_2 + a_2 * b_2 * c_2 * d_1 ) / (d_1*d_2)
Let's try it on your numbers.

(400*.6*801/1004) + (150*.6*117/117) = 191,47 + 90 = 281,47

(400*.6*801*117 + 150*.6*117*1004) / (*117) = (22492080 + 10572120) / 117468 = 33064200 / 117468 = 281,47

You're welcome!

If you do not manage to produce a formula for a sum of "n" such sets of numbers, let me know and I'll write it on the paper, scan it for you, and stick it here.