A wall is to be built in a room.
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A wall is to be built in a room. One person starts working on the first day with a certain efficiency. On the second day, he is joined by one more person. On the third day, one more person joins the work and all three work with three times the efficiency as that of a single person. The process continues and the wall is finally built in $n$ days. Instead, if $n$ persons had worked together on building the wall with uniform efficiency, the wall could have been built in $15x$ days. What is the value of $n$?
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Accurate technical and quantitative evaluation based on foundational principles.
Step-by-step Derivation:
Step 1: Formulate problem conditions.
Step 2: Apply logical deduction.
Step 3: Conclude correct option.