Question

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 b

• A. 86
• B. 84
• C. 78
• D. 80

Answer 1

The Correct Option is B

Given that, initially number of matches team has played =40

The number of matches won by team =30% of 40=\(\frac{30}{100}×40\)=12

Let the remaining matches be x.

The number of remaining matches won by team =60% of

\(x=\frac{60}{100}× x=0.06x\)

simplifies :
\(=12+1.2x=40+x\)
\(=0.2x=16\)
\(=x=\frac{16}{0.2}\)
\(x=80\)
When the team won 90% of the remaining matches.

Then, the number of remaining matches won by the team 90% of 
\(80=\frac{90}{100}×80=72\)
The total number of matches won by the team in the tournament 

\(=12+72=84\)

so, correct answer is: 84.

Answer 2

We know that out of the 40 matches that have been played, 30 have been won. 
The overall win percentage is 50% if the last 60% of the matches are won.
Let 'x' be the total number of games to be played.
\(0.5 \times 40 + x = 0.3 \times 40 + 0.6 \times x\)
\(0.6x + 0.3 \times 40 = 0.5 \times (40 + x)\) 
\(12 + 0.6x = 20 + 0.5x = 8x = 80\)
\(⇒ x = 80\)
After they won, 90% of what was left \(= 80(0.9) = 72 \)
Thus, 84 wins in total.