# Thread: splitting profits by percentages

1. ## splitting profits by percentages

Hi, any help would be great.

I need to work out a way of splitting different percentages of a profit between people.

Example #1:
Ten people split the profit (£1000) between them. But not equally.
4 people (A-D) need to get 30% more than the other 6 people (E-J).
I have worked this out manually as:
A 11.6% £116.00
B 11.6% £116.00
C 11.6% £116.00
D 11.6% £116.00
E 8.93% £89.30
F 8.93% £89.30
G 8.93% £89.30
H 8.93% £89.30
I 8.93% £89.30
J 8.93% £89.30
(£1000.00)

Is there an equation to work this out?

I need to work out many more percentage splits and by different amounts of people.

Example #2:
Ten people split the profit between them. But not equally.
3 people (A-C) need to get 40% more than the other 7 people (D-J).

...I could work it out manually... But I need it as an equation so i can change the number of people who receive more and the percentage relative to the others that they receive. I will also need to work this out for 8 people and 6 people etc... and get it into a Exel spreadsheet!

Thanks,
Scott

Let :
money received by A-D each = x
money received by the rest = y

x = 1.3 y----------> equation 1, because x is 30 % higher than y

4x + 6y = 1000---> equation 2

you can replace 4 or 6 with the number of people you desired

3. General case (with example using your first one):

a = amount (1000)
t = total persons (10)
n = number of persons getting MORE (4) ; n < t
r = percent MORE (30)
x = lower amount (?)

x = a / (t + nr/100)

x = 1000 / (10 + 4(30)/100) = 89.2857... (you got 89.30)