Given that, initially number of matches team has played $=40.$
The number of matches won by team $= 30\%$ of $40 = \frac{30}{100} \times 40 = 12$
Let the remaining matches be $x.$
The number of remaining matches won by team $= 60 \%$ of $x = \frac{60}{100} \times x = 0.06x$
Now, $\frac{12+0.06}{40+x} = \frac{50}{100}$
$\Rightarrow \frac{12+0.06}{40+x} = \frac{1}{2}$
$\Rightarrow 24+1.2x = 40+x$
$\Rightarrow 0.2x = 16$
$\Rightarrow \boxed{x = 80}$
When the team won $90\%$ of the remaining matches.
Then, the number of remaining matches won by the team $90\%$ of $80 = \frac{90}{100} \times 80 = 72$
$\therefore$ The total number of matches won by the team in the tournament $= 12+72 = 84.$
Correct Answer $:\text{B}$