From first part of the question

Rate of work per person =( A (units of work)/( A (days) ×A (hrs)×A (people)).

Now translating it to B people, B days and B hrs after assuming each and every person works at the same speed.

Rate of work =

(A (units of work)×B (people)/A (people))/(( A (days)×A (hrs)×(B (hrs)/A (hrs))×(B (days)/A (hrs)))

Here (B/A) terms alters both the (units of work) term and (total time) terms appropriately ie., it linearly alters those terms.

Since we need work, this equation has to be multiplied with total time and can be reduced to

Work = [A (units of work) × (B (people)/A (people))]