Find the ratio of twelfth terms if the sum of first n terms of two AP's are $3n+8,7n+15$ 
The sum of first n terms of two AP's are $3n+8,7n+15$. Then the ratio of their twelfth term is:

$$
\frac{a_{12}}{A_{12}}=\frac{a+11d}{A+11D}=\frac{2a+22d}{2A+22D}=\frac{s_{23}}{S_{23}}=\frac{3(23)+8}{7(23)+15}=\frac{77}{176}=\frac{7}{16}
$$
Fine but if I do the following
$$
a_{12}=s_{12}-s_{11}=44-41
=3\\
A_{12}=S_{12}-S_{11}=99-92=7\\
\frac{a_{12}}{A_{12}}=\frac{3}{7}
$$
Why am I getting diferent results for method 1 and 2 ?. Is the question wrong because the sum of terms of AP is a quadratic expression in $n$ ?
Note: This was asked as a multiple choice question with options including both the results of method 1 and 2.

The question should have been 

The ratio of the sum of first $n$ terms of two AP's are $3n+8:7n+15$

instead of

The sum of first $n$ terms of two AP's are $3n+8,7n+15$

