For the past n days, the average (arithmetic mean) daily pro

Nothing wrong with your equation; something went wrong when you simplified the equation.

\(55 = \frac{50n+90}{n+1}\)

\(55n+55=50n+90\)
\(5n=35\)
\(n=35/5=7\)

Ans: "E"

The problem in your calculation has already been identified above.

Let me discuss the concept of average in another way:
It helps to think of average as the number that makes all the numbers equal. That is, if I say average of 4 numbers is 50, the first thing you should do is imagine having 4 numbers, each of them 50. Most probably, all of them will actually not be equal to 50 but the overall effect would be the same as if they were 50 each because their sum would be 200.

So when you say that for n days, production was 50 on average, I imagine the production of each day as 50. If on (n+1)th day too, the production is 50, the average will remain the same i.e. 50. But actually, the production is 90. i.e. 40 extra. To get to the average, we divide the sum equally among all. So the 40 extra needs to be divided equally among all the days including the (n+1)th day. Since the average increases by 5 (becomes 55), it means there must have been a total of 8 days (because 40/8 = 5). So n must be 7.

Number line:

Old---------Change--------------New
50----------55--------------------90
55-50 = 5
90-55 = 35
35/5 = 7

I can't really explain this but Karishma's explanation does.