Find the ratio between the number of goals sored by team B in its match against team C to the number...........

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.

Find the ratio between the number of goals sored by team B in its match against team C to the number of goals scored by team A in its match against team C

2 : 1

3 : 1

4 : 3

3 : 4

Cannot be Determined

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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
Number of goals scored by Team B in its match against team C = 6
Number of goals scored by Team A in its match against team C = 2
Required ratio = 6 : 2 = 3 : 1
Hence, option 2 is the correct answer.