Let's say a1,...,an are daily productions for the past 1...n days accordingly.

Then average for the past n days is (a1+...+an)/n = 50

Average for the past n days AND today will be
(a1+...+an+90)/(n+1) = 55

Left part is equal to
(a1+...+an)/(n+1)+90/(n+1)=(a1+...+an)*n/n(n+1)+90/(n+1)= (50n+90)/(n+1)

Now you need to solve this equation: (50n+90)/(n+1) = 55

I am not the best Maths guy. But here is a more simple way to get the answer

x/n=50
Therefore x=50n

x+90/ n+1 = 55

now substitute for X, then you get

50n + 90 / n+1 = 55

Resulting into n = 7

See image

See image

You can treat this as a mixture problem and get the answer as:-

(90-55)/(55-50)=n/1, Solving we get n = 7.