Can anybody please decompose this phrase and explain its meaning by providing some examples and explicate the context it could be used.
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It is used when you gradually make progress in some field and reach your goals. It is also indirectly implying the hardships that one has to face in order to reach the goal, and restating that there isn't a 'short-cut'.
He started out as a secretary, but worked his way up and eventually became a manager.
In spite of having started his career as a bus conductor, Rajnikanth has worked his way up to become one of the biggest stars in the film industry.
Often it is also used in conjunction with 'ladder'
I'll have to work my way up the corporate ladder.