Question 825889
I'm not sure what method you used to work out your answer, but this is how I would do it.

Av age for 6 children is 13 yrs and 5 mths.
Sum of all their ages is 6*(13 yr + 5 mths) = 78 yrs + 30 mths

Av age for 7 children is 13 yrs and 7 mths  (an increase of 2 mths)
Sum of all their ages is 7*(13 yr + 7 mths) = 91 yrs + 49 mths

The difference in the two totals must be the age of the 7th child.

(91 yrs + 49 mths) minus (78 yrs + 30 mths) = 13 yrs and 19 mths

So age of 7th child is 14 yrs and 7 mths