Let A ={ n ∈ N: n is a 3-digit number } B={9 k +2: k ∈ N } and C ={9 k +l: k ∈ N } for some l(0<l<9) If the sum of all the elements of the set A ∩( B…

Let $\displaystyle \mathrm{A}=\{\mathrm{n} \in \mathrm{N}: \mathrm{n}$ is a $\displaystyle 3$-digit number $\displaystyle \}$ $$B=\{9 \mathbf{k}+2: \mathbf{k} \in \mathbf{N}\} $$ and $\displaystyle \mathrm{C}=\{9 \mathrm{k}+l: \mathrm{k} \in \mathrm{N}\}$ for some $\displaystyle l(0<l<9)$ If the sum of all the elements of the set $\displaystyle \mathrm{A} \cap(\mathrm{B} \cup \mathrm{C})$ is $\displaystyle 274 \times 400$, then $\displaystyle l$ is equal to \_\_\_\_.