A team has played 40 matches, winning 30% of them. If they win 60% of the remaining matches in a tournament, what will their total number of wins be? If they win 90% of the remaining matches, what will their total number of wins be?

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Question matches

Solution :-

A team has played 40 matches, winning 30% of them. Let the total number of matches in the tournament be T, and the remaining matches be R = T - 40.

Matches won so far: 30% of 40 = 12.

If they win 60% of the remaining matches:

New total wins = 12 + 0.6R

Given that their overall win percentage is 50%:

(12 + 0.6R) / T = 0.5

Since T = 40 + R:

12 + 0.6R = 0.5(40 + R)

12 + 0.6R = 20 + 0.5R

0.1R = 8 → R = 80

Thus, T = 40 + 80 = 120.

If they win 90% of the remaining matches:

Total wins = 12 + 0.9R = 12 + 0.9(80) = 12 + 72 = 84.

Answer: 84 matches.

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