Share of the profits for partnerships?

Question

I am studying for my exam in Advanced Bookkeeping and accountancy and still cannot get my head around this sharing of the profits. For example:

Mary Jackson was asked to join the existing partnership of Peter Smith and Pat Jones. Goodwill was valued at 21000 at the date Mary Joined. In the original partnership of Peter Smith and Pat Joines Profits were shared in the ratio 3:4 respectively. After Mary Jackson joined partnership the profit is to be shared 3:3:2 between Peter Smith:Pat Jones:Mary Jackson.

The answers are
Goodwill DR 21000
Capital-Peter Smith 9000 cr
-Pat Jones 12000 cr

Capital -Peter Smith 7875 dr
- Pat Jones 7875 dr
- Mary Jackson 5250 dr

Goodwill - 21000 cr

Can someone please explain if there is an easier way of working out how they got the answers to the question or not?

How is 21000 devided for the share in the profits by ratio.

Answer 1

Before she joined, the old partners shared profits in this ratio 3:4, i.e. there were 7 parts, Peter had 3 parts and Pat had 4 parts. If you're told goodwill is $21,000, then to allocate the goodwill to Peter, you take 3/7 x 21,000 = 9,000. And to allocate the goodwill to Pat, you take 4/7 x 21,000 = 12,000.

Then after Mary joined, the ratio became 3:3:2, i.e. there were 8 parts; Peter had 3 parts, Pat had 3, and Mary had 2. So to allocate back the goodwill to remove it from the a/cs, for Peter you take 3/8 x 21,000 = 7,875, same for Pat cos he also has 3 parts, and Mary gets 2/8 x 21,000 = 5,250.

Is it clearer now?