We shall finish the work __________ a week.
Tripura Public Service Commission - 2019,
Answer: B
The preposition is within: We shall finish the work within a week.
Within means "before the end of" a period: the work will be completed at some time during the coming week, no later.
In a week usually means "after a week from now" or "taking a week", not "before a week is over", and after a week sets the finish later still. On is used with days and dates, not with a length of time.
So within a week answers "by when?" (any time up to seven days), while in a week answers "how soon?" or "how long?", which is why it is the near miss.
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