Q$\mathrm{.}21$ In a transitional curve on $BG$ track, the speed by Railway Board formula is $V_{\text{m}\text{a}\text{x}}=4\mathrm{.}35\sqrt[\phantom{2}]{R-67},$ which is $1\mathrm{.}25$ times maximum permissible obtained by cant formula. Calculate the radius of curve if cant deficiency is $7\mathrm{.}6cm.$

$($a$)694m$

$($b$)512m$

$($c$)820m$

$($d$)112m$