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

Options

A. `2:1`
B. `3:1`
C. `4:3`
D. `3:4`

Explanation

To solve the problem step by step, we will analyze the matches one by one and derive the necessary information.

### Step 1: Analyze the A vs B Match
- **Outcome**: B wins the match.
- **Points scored by B**: 4 points.
- **Goals scored by A**: 2 goals (none from outside).

**Points Calculation for B**:
- A scored 2 goals, so B concedes 2 goals, resulting in a penalty of 2 points (1 point for each goal conceded).
- Therefore, the points B scored can be calculated as:
\[ \text{Points scored by B} = \text{Total Points} + \text{Penalty} = 4 + 2 = 6 \]
- Since B scored 6 points and the scoring system gives 2 points for a goal, B must have scored:
\[ \text{Goals scored by B} = \frac{6}{2} = 3 \text{ goals} \]

### Step 2: Analyze the A vs C Match
- **Outcome**: C scored 0 points.
- **Points scored by A**: 4 points.
- **Goals scored by A from outside**: 1 goal.

**Points Calculation for A**:
- A scored 1 goal from outside (3 points) and 1 goal from inside (2 points), so:
\[ \text{Total Points for A} = 3 + 2 = 5 \]
- Since C scored 0 points, A must have scored:
\[ \text{Goals scored by C} = 0 \text{ (which means A scored 2 goals)} \]

### Step 3: Analyze the B vs C Match
- **Points scored by B**: 6 points.
- **Goals scored by C**: 1 goal more than B.

**Points Calculation for B**:
- Since B scored 6 points, we can deduce:
\[ \text{Goals scored by B} = \frac{6}{2} = 3 \text{ goals} \]
- Let the goals scored by C be \( x \). Thus:
\[ x = 3 + 1 = 4 \text{ goals} \]
- Since none of the goals scored by C were from outside, the total points for C would be:
\[ \text{Points for C} = 2 \times 4 - 3 = 5 \text{ (due to 3 goals conceded)} \]

### Step 4: Calculate the Ratio
- Goals scored by B against C: 3 goals.
- Goals scored by A against C: 2 goals.

**Ratio Calculation**:
\[ \text{Ratio} = \frac{\text{Goals scored by B}}{\text{Goals scored by A}} = \frac{3}{2} \]

### Final Answer
The ratio between the number of goals scored by team B in its match against team C to the number of goals scored by team A in its match against team C is:
\[ \text{Ratio} = 3:2 \]