Why does ##Sigma T. x=0## hold for tension

Kashmir
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Homework Statement
Found it on internet, couldn't understand why it works
Relevant Equations
$Sigma T. x=0$
1686882109818.png
 
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Consider the work done on the (ideal) pulleys.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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