A bank in Cork, Ireland has $400$ million in assets in the $0$ percent risk weight category, $1000$ million in assets in the $20$ percent risk weight category, $5000$ million in assets in the $50$ percent risk weight category and $8000$ million in assets in the $100$ percent risk weight category. This bank has $685$ million in core $($Tier $1)$ capital $($e$.$g$.,$ common and preferred equity$)$ and $115$ million in Tier $2$ capital $($e$.$g$.,$ allowance for loan & lease losses or ALL, subordinated debt, etc.$).$ What is this bank's ratio of Tier $1$ capital to risk$-$weighted assets?

A$.$

$6\mathrm{.}25$ percent

B$.$

$6\mathrm{.}40$ percent

C$.$

$6\mathrm{.}35$ percent

D$.$

$1\mathrm{.}07$ percent

E$.$

$7\mathrm{.}48$ percent