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In a tournament, a team has played $40$ matches so far and won $30 \%$ of them. If they win $60 \%$ of the remaining matches, their overall win percentage will be $50 \%.$ Suppose they win $90 \%$ of the remaining matches, then the total number of matches won by the team in the tournament will be

1. $80$
2. $84$
3. $78$
4. $86$

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 $:\text{B}$
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