BPP Practice & Revision Kit 8b.8 page 66

Hi John,
Please can you help me with this question:
Two joint products A and B are produced in a process. Data for the process for the last period are as follows:
Product A B
Tonnes Tonnes
Sales 480 320
Production 600 400
Common production costs in the period were $12,000. There was no opening inventory. Both products had a gross profit margin of 40%. Common production costs were apportioned on a physical basis.
What was the gross profit for product A in the period?
$2,304; $2,880; $3,840; $4,800

BPP shows the answer is $3,840. My calculation is $4,800 which is shown below:
12,000 x (600/1000) = 7200 (production cost of A);
Equation: sales value x 0.4= profit; sales value x 0.6= production cost.
Therefore, sales value= 7200/0.6; profit= (7200/0.6)x 0.4= 4800
Why do we need to match production cost against sales? 7200x 480/600= 5760; 5760x 40/60= 3840. Just can’t get my head around it.

Many Thanks