AT Kearney mock question

Question

Hi, I'm having a problem with one of the AT Kearney mock exam questions. Can you please suggest a solution and your rationale? Thanks!

Question: At a school fair, Ana sells cookies prepared by her mother. Ana buys the cookies for 115% of the costs her mother pays to make them. Ana’s profit margin is 30%. What share of her mother’s cost is Ana’s profit?

Answer 1

What share of her mother’s cost is Ana’s profit?

=> Her mothers costs are 100%. We need to find Ana's Profit relative to those 100%.

Ana’s Profit (relative to her mothers cost) = Revenue - Cost = Revenue - 115% = ???

We can calculate Ana's Revenue by using the calculation formula for her Profit Margin:

Profit Margin = Profit / Revenue
Profit Margin = (Revenue - Cost) / Revenue
30% = (Revenue - 115%) / Revenue
30% * Revenue = Revenue -115%
70% * Revenue = 115%
Ana’s Revenue = 164,29% (rel. to her mothers cost)

This means Ana sells the cookies for 164,29% of the price that her mother paid to prepare them.

Ana’s Profit relative to her mothers cost is therefore: Profit = Revenue - Cost = 164,29% - 115% = 49,29%

Answer 2

Hi Jan,

It seems like an uncommon ratio to calculate, but iIwould try the following:

Let's say her Mom had 100 dollar in costs >> sell to Ana for 115 dollar (=115%)
Ana's profit margin is 30% (I assume of her revenue) >> so her costs are 70% of revenue >> 100% revenue is around 164 dollars
That leaves a profit of 164-115= roughly 50 dollars
Which makes the share: 100/50 = around 50%

Does this help?