What is the maximum possible sum of the total number of goals scored by those players of all three t...........

Quantitative Aptitude (SBI-PO) Case Studies

Direction: Study the given information carefully and answer the following questions.
There was a football tournament of three teams i.e. A, B and C in which each team played 2 matches.
Score pattern of the tournament is:
• A team gets 2 points for scoring a goal against the opponent team.
• A team gets 3 points for scoring a goal against the opponent team from the outside area.
• There is a penalty of 1 point if a team concedes a goal.
• Only three players from each team scored the goals.
A – B Match: B is the winner of this game. Total points scored by B in this match is 4 . Also, team A scored 2 goals and none of the players scored the goal from the outside area.
A – C Match: C scored 0 points in the match. Only one player from team A scored a goal from outside area. A scored 4 points in this match.
B – C Match: B gets 6 points from match. Team C scored 1 goal more than Team B. One player from team B scored a goal from outside area but none from team C.

What is the maximum possible sum of the total number of goals scored by those players of all three teams, who score more than one goal in a tournament?

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Explanation:

A – B match:
Total points scored by B = 4
And total goals scored by A = 2
So, 2 points must have been subtracted from B’s score, as it conceded 2 goals.
i.e., Actual points scored by B without penalty = 4 + 2 = 6
Also, it is given that none of the players scored from the outside area.
So, total number of goals scored by B in the match = 6/2= 3
i.e., B scored 3 goals and A scored 2 goals in the match.
Points scored by A in this match = 2 × 2 – 3 = 1
A – C Match:
C scored 0 points in the match and only one player from team A scored a goal from outside area. And A secured 4 points from this match.
Given, 1 goal was scored by Team A from outside area. So, points from this goal = 3
But team A has secured 4 points.
So, it must have scored 1 more goal against C and also team A must concede 1 goal to make its points 4.
So, team C scored 1 goal in this match.
i.e., A scored 2 goals (out of which one was from outside area) and C scored 1 goal in the match.
B – C Match:
B gets 6 points from the match. Team C scored 1 goal more than team B. One player from team B scored a goal from outside area
Let number of goals scored by B = P
And number of goals scored by C = P + 1
Since, one player from team B scored a goal from outside area. So, total points scored by B would be:
2P + 1 – P – 1 = 6 (because B conceded (P + 1) goals, So, (P + 1) need to be subtracted)
i.e., P = 6
So, Team B scored 6 goals and team C scored 7 goals in the match.
Points scored by team C = 2 × 7 – 6 = 8
Now, Total points scored by Team A = 1 + 4 = 5
Total points scored by Team B = 4 + 6 = 10
Total points scored by Team C = 0 + 8 = 8
Total number of goals scored by Team A = 2 + 2 = 4
Total goals scored by Team B = 3 + 6 = 9
Total goals scored by Team C = 1 + 7 = 8
Since, it is given that 3 players from each team scored a goal.
So, maximum goals that can be scored by a single player in team A = 2
Similarly, for team B it is = 7
And for team C = 6
Required Answer = 2 + 7 + 6 = 15
Hence, option 4 is correct.