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

$84$

$78$

$86$

$80$

✅ Correct Option: 1

The team has played 40 matches and won 30% of them.

Matches won = 30% of 40 = 0.30 × 40 = 12 matches

Let's call the number of remaining matches x.

If they win 60% of these remaining matches, they'll win 0.6x additional matches.

Total matches won = Current wins + Future wins

= 12 + 0.6x

Total matches played = Current matches + Remaining matches

= 40 + x

For a 50% overall win rate:

$\frac{\text{Total matches won}}{\text{Total matches played}} = 0.50$

$\frac{12 + 0.6x}{40 + x} = 0.50$

Cross-multiply:

$12 + 0.6x = 0.50(40 + x)$

$12 + 0.6x = 20 + 0.5x$

$12 + 0.6x - 0.5x = 20$

$12 + 0.1x = 20$

$0.1x = 8$

$x = 80$

So there are 80 remaining matches in the tournament.

Now we can answer the actual question: If they win 90% of the remaining matches, how many total matches will they win?

Current wins: 12 matches

Additional wins at 90% rate: 90% of 80

= 0.90 × 80 = 72 matches

Total matches won = 12 + 72 = 84 matches

Therefore, the team will win 84 matches in total.

When dealing with percentage problems involving future scenarios, we always identify what stays constant (the matches already played) and what changes (the performance in remaining matches). Setting up the equation using the given condition helps us find the missing information we need.

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