Question

A football team played some number of games in a season in which the team won 10 games and lost 5 games. If a football team wins the remaining number of games of the season, it will have won 80 percent of its games. How many games in total will have been played in the season?
(A) 15
(B) 25
(C) 30
(D) 20

Answer 1

Hint: Assume that total number of games played be x. So, the total number of games won will be \[x - 5\]. According to the question $80\% \times x = x - 5$.We solve the equation by taking the number containing $x$ variable on one side and constant on the other side. By solving we got our answer.

Complete step-by-step answer:
In the question it is given that
Number games lost = 5
Number of games win = 10
Let us take the total number of games be x
$\therefore $Number of win game =$x - 5$
According to the question:
$ \Rightarrow 80\% \times x = x - 5$
$ \Rightarrow \dfrac{{80}}{{100}} \times x = x - 5$
After simplifying the equation we get,
$ \Rightarrow \dfrac{4}{5} \times x = x - 5$
Now we solve equation taking terms having x variable on one side and constants on the other
$ \Rightarrow \dfrac{4}{5} \times x - x = - 5$
We take LCM of 5 in LHS
$ \Rightarrow \dfrac{{4x - 5x}}{5} = - 5$
$ \Rightarrow \dfrac{{ - x}}{5} = - 5$
Cross multiply
$ \Rightarrow - x = - 5 \times 5$
$ \Rightarrow - x = - 25$
$ \Rightarrow x = 25$
The total number of games played in the season is 25.

So, the correct answer is “Option C”.

Note: This question has an alternative solution as well. Let us now discuss the alternative solution:
Given:
Number of win game =10
Number of lost game =5
$ \Rightarrow $Lost game percentage= 100 – win percentage
= $100\% - 80\% $
= $20\% $
$ \Rightarrow $Percentage of 5 lost game = $20\% $
$ \Rightarrow $Percentage of 1 lost game =$\dfrac{{20}}{5}$
                  =$4\% $
$ \Rightarrow $Percentage of already won game =$10 \times 4\% $
               = $40\% $
$ \Rightarrow $Remaining match percentage = $80\% - 40\% $
                             = $40\% $
$ \Rightarrow $Remaining matches to be won = $\dfrac{{40\% }}{{4\% }}$
                               =10
$ \Rightarrow $Matches already won = 10
$ \Rightarrow $Total number of matches won = $10 + 10 = 20$
$ \Rightarrow $Total number of matches lost =5
$\therefore $Total number of matches = Total number of matches won in Total number of matches lost
=$20 + 5 = 25$
The total number of games played is 25.