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

The problem states that the team has played 40 matches so far and won 30% of them. This means they have won 12 matches (30% of 40 is 12).

The problem also states that if they win 60% of the remaining matches, their overall win percentage will be 50%. This allows us to find out the total number of matches in the tournament. Let's denote the total number of matches as T and the remaining matches as R. We know that:

(12 + 0.6R) / T = 0.5

We also know that the total number of matches T is equal to the matches played so far plus the remaining matches:

T = 40 + R

Substituting the second equation into the first gives us:

(12 + 0.6R) / (40 + R) = 0.5

Solving this equation for R gives us R = 20. So, there are 20 remaining matches.

The problem then asks us to find out how many matches the team will have won if they win 90% of the remaining matches. This is simply 90% of 20, which is 18.

So, the total number of matches won by the team in the tournament will be the matches they've already won (12) plus the matches they win out of the remaining (18), which is 12 + 18 = 30.

The problem states that the team has played 40 matches so far and won 30% of them. This means they have won 12 matches (30% of 40 is 12).

The problem also states that if they win 60% of the remaining matches, their overall win percentage will be 50%. This allows us to find out the total number of matches in the tournament. Let's denote the total number of matches as T and the remaining matches as R. We know that:

40 + R = T (since the total number of matches is the sum of the matches played so far and the remaining matches)

We also know that if they win 60% of the remaining matches, their overall win percentage will be 50%. This means that:

(12 + 0.6R) / T = 0.5 (since the total number of wins is the sum of the wins so far and 60% of the remaining matches, and this divided by the total number of matches gives the overall win percentage)

We can substitute the first equation into the second to get:

(12 + 0.6R) / (40 + R) = 0.5

Solving this equation gives R = 20. So, the total number of matches in the tournament is 40 + 20 = 60.

Finally, the problem asks for the total number of matches won by the team if they win 90% of the remaining matches. This would be:

12 (matches won so far) + 0.9 * 20 (90% of the remaining matches) = 12 + 18 = 30 matches.