We call:

a - the youngest brother

b - the 2nd young brother

c - the third young brother

d - the oldest brother

We have:

a + b + c + d = 1200 that \(\left(d-300\right)+\left(d-200\right)+\left(d-100\right)+d=1200\)

<=> \(\left(d-300\right)+d=\left(d-200\right)+\left(d-100\right)=1200:2=600\)

=> \(d=450\) 

=> \(d-100=350=c\)

=>\(d-200=250=b\)

=>\(d-300=150=a\)

Arrcoding to the solution, the youngest brother (a) gets 150.

ANSWER: 150

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