Question 57

The Guava club has won 40% of their football matches in the Apple Cup that they have played so far. If they play another n matches and win all of them, their winning percentage will improve to 50. Further, if they play 15 more matches and win all of them, their winning percentage will improve from 50 to 60. How many matches has the Guava club played in the Apple Cup so far? In the Apple Cup matches, there are only two possible outcomes, win or loss; draw is not possible.

Solution

Let 'm' be the number of matches Guava played till now. They won '0.4m' matches. 

After playing another 'n' matches and wining all of them, their winning percentage will improve to 50.

i.e, 

$$\ \frac{\ 0.4m+n}{m+n}=0.5$$  

 $$m=5n$$

Playing 15 more matches and wining all of them, their winning percentage will improve from 50 to 60.

i.e $$\ \frac{\ 0.4m+n+15}{m+n+15}=0.6$$

Solving, we get $$6+0.4n\ =\ 0.2m$$

Substituting $$m=5n$$,

we get $$6+0.4n\ =\ n$$ 

$$n=10\ \&\ m\ =50$$

Hence, Guava club played 50 matches so far. 

The answer is option A.

Video Solution

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