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Directions: In a football tournament. There are four football teams Chennai, Mumbai, Delhi, and Kolkata each will play against each other Two times.
1. One match will be in-home and another match will be away.
2. Each team will get 2 game points when they hit a goal and they will lose 1 game point when they concede a goal.
3. A team will get 5 points in winning a game. To qualify for finals a team should get above 10 points.
Note:
(i) Team Chennai won 3 matches Mumbai won 5 matches and Delhi and Kolkata have won the remaining matches equally.
(ii) Two match between Kolkata and Delhi is drawn due to the equal number of goals.
In a match, Mumbai won Delhi by the difference of 6 points and Delhi got 2 points to find the ratio of goals scored by Mumbai and Delhi.
3 : 2
9 : 4
8: 3
4 : 5
1 : 1
Let’s break it down step by step:
- Total matches: With 4 teams, each team plays every other team twice—so 6 pairs × 2 matches = 12 matches total.
- Match wins: Chennai won 3, Mumbai 5, leaving 4 matches; those are split between Delhi and Kolkata, so 2 each.
- Draws: The 2 matches between Delhi and Kolkata were draws.
- Points system:
- Goal scored = +2 game points
- Goal conceded = -1 game point
- Win = 5 match points
- Mumbai vs Delhi: Mumbai wins by a 6-point difference. Delhi got 2 points (from goals/goals minus conceded), so Mumbai must have gotten 2 + 6 = 8 points from goals.
- Translating that to goals:
Let's call Mumbai’s goals = M, Delhi’s goals = D.
- For Delhi: 2 = 2D - M
- For Mumbai: 8 = 2M - D
- Solve these:
- D = (2 + M) / 2
- Substitute D in Mumbai’s equation: 8 = 2M - ((2 + M) / 2)
- 8 = 2M - 1 - M/2
- Multiply whole equation by 2:
16 = 4M - 2 - M
16 + 2 = 4M - M
18 = 3M ? M = 6
- D = (2 + 6) / 2 = 4
- So, the ratio of goals scored: Mumbai : Delhi = 6 : 4 = 3 : 2
- Let’s look at the options:
- Option 1: 3 : 2
- Option 2: 9 : 4
- Option 3: 8 : 3
- Option 4: 4 : 5
- Option 5: 1 : 1
- That makes option 1 (3:2) the correct answer.
By: Parvesh Mehta ProfileResourcesReport error
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