Q$.21$ 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 $7\mathrm{.}6$ cm $.$

$($a$)694$ m

$($b$)512$ m

$($c$)820$ m

$($d$)112$ m