The average of 12 numbers is M and the average of 8 of these numbers is P. If the average of the remaining numbers is N, then which of the following options is correct?

The average of 12 numbers is M.

Sum of 12 numbers = $$12\times M$$ = 12M    Eq.(i)

The average of 8 of these numbers is P.

Sum of 8 of these numbers = $$8\times P$$ = 8P    Eq.(ii)
If the average of the remaining numbers is N.

average of the remaining (four numbers) = $$4\times N$$ = 4N    Eq.(iii)

Eq.(i) = Eq.(ii)+Eq.(iii)

12M = 8P+4N

3M = 2P+N

The obtained equation is available in option (a). So this is the correct answer.