Unable to understand a solved problem: Impulse & Impulsive force.

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Why the acceleration $f$ of $m$ to the attached solution of the problem has been taken as $\frac{m-M}{m+M}g$.

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Since masses $m$ and $M$ are pulling in opposite directions, force acting on the system is $F = (m-M)g$ (these are just gravitational forces). The mass of the system is $m+M$, so by Newton's second law we have $$(m+M)f = (m-M)g$$