# Work out percentages and commisions

I have a price 265.69 top price. Of this 265.69, 180.83 is cost. 45 is profit 13.29 is a commission at 5% of price and 26.57 is another commission at 10% of the price

180.83 + 45 + 13.29 + 26.57 = 265.69

if I minus 5% from the price, the price becomes 252.41

the commissions are set to now 8% and 4% so commission 1 will be 20.20 and commission 2 will now be 10.10 leaving a profit of 41.28

my question is if I sell the product at 260.00 how will I split the difference of the extra amount so each gets there rightful share. what will the percentages be of each of the two commissions, if at 252.41 comm1 must get 8% and comm2 4%

if I minus another 5% from 252.41 I get 239.79. now each comm: comm1 must be 5% of sale price and comm2 must be 3% of sale price. and the same thing will apply if the product is sold at 245 for example. what will the calculation be so each gets their fair split according to the pre-determined percentages

• I know this should be really simple to work out but I cannot figure out how to amend the percentages according to the price sold at above the 5% discount of full price Commented Oct 23, 2014 at 14:22
• Do you want to maintain the profit when you sell it at 260? Commented Oct 23, 2014 at 14:31
• No the profit will decrease according to the pre determined percentages. so cost is 180.83, comm1 is 10% at full price and comm2 is 5% at full price and profit is 45 at full price which gets to the amount of 265.69. now at a 5% mark down comm1 is set to 8% and comm2 is set to 4% leaving the remaider of (265.69 - 5%) minus the comms on 252.41. so comm1 here would be 20.20 comm2 would be 10.10 leaving a profit of 41.28 Commented Oct 23, 2014 at 15:34

If I understand the problem correctly, you would want to set the ratio of commissions at a predetermined level just like you had 10% and 5% and later you had set it at 8% and 4% and so on. Let us call commission 1 as x% and commission 2 as y%.

Let us call the ratio of $\frac{x\text{%}}{y\text{%}} = r$

Then the equation is Price $P = (Cost C) + (r\times y\times P) + (y\times P) + (Profit)$.

What is known here are P, C, x and y.

What is derived here are Profit and r.

Let us take the example of 265.69, here $\frac{10\text{%}}{5\text{%}} = 2$

Now $Price = 180.83 + 2\times \frac{y}{100} 265.69 + \frac{y}{100} 265.69 + Profit$

Now substitute y, and you get the profit = 45

Now convert Profit as a percentage of Price and be equal to p = Profit/Price.

For any amount $P_1$, you can derive y and x if you would want to maintain r and p.

$252.41 = 180.83 + [2.(0.04) + 0.04]*252.41 + 41.28 \tag1$

$=> P = 41.28$, and hence $p = 41.28/252.41 = 16.35$%

$260 = 180.83 +[2*(y) + y] * 260 + .1635*260 \tag2$

Subtract (1) from (2)

$7.59 = 3*\frac{y}{100}*260 +42.51 - 30.29 - 41.28$

$y = 4.698$%

$x = 9.397$%

• Thank you Satish. If i look at your calculation - =>P=45, and hence p=45/252.41=17.83% profit here should be 41.28 and not 45 because it is a 5% mark down with comm now at 8% and comm2 at 4%? A 5% mark down from 265.69 Commented Oct 23, 2014 at 15:29
• You are right, it should be 41.28. You have given so many numbers that I mistyped it. I will edit it. Commented Oct 23, 2014 at 15:41