Direction: At MERI Kolkata students stay in different Sadans namely Bose, Diesel, Edison, Faraday, Marconi, and Rankin. Students who stay in these sadans represent their sadan in Foot Ball tournament. 1st stage of the tournament is conducted in 5 days from Monday to Friday such that everyday each team played exactly 1 match. As per the rule 3 points> are awarded for a win, 0 for a loss and each team gets 1 point for a tie. On Wednesday evening due to some unavoidable reason tournament is postponed. When Officer In charge sports Mr. A B Halder asked the update of tournament he got the following information.
(i) Maximum number of goals scored by a team in a match is 4
(ii) No team lost with a goal difference more than 2
(iii) In each match at least 1 goal is scored.
(iv) Total number of goals made by the teams are Bose (11), Diesel (9), Edison ( = 5), Faraday ( = 1), Marconi ( = 7), and Rankin ( = 4)
(v) Total number of goals against the teams are Bose (5), Diesel (9), Edison ( = 7), Faraday ( = 4), Rankin ( = 5)
(vi) Faraday won match while Marconi and Rankin got 4 and 3 points respectively.
(vii) On Monday Bose played against Diesel.
(viii) On Tuesday Diesel won a match against Edison with a goal difference of 2
(ix) On Wednesday Edison won a match in which total number of goals scored is 2.
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What is the total number of points given to these teams in these 3 days?
-
- 28
- 27
- 26
- None of these
Correct Option: C
Since total number of goals scored and goals against is same hence we can find goals against Marconi which is (11 + 9 + 5 + 1 + 7 + 4) – (5 + 9 + 7 + 4 + 5) = 37 – 30 = 7. Since Bose sadan scored 11 goals while goals against is 5 it is possible when all the matches are won with (3-1) (4-2) and (4-2)
Since Marconi got 4 points which is possible with 1 win (3 points) 1 draw (1 point) and 1 loss (0 point) Similarly Rankin got 3 points and also Goals for is 4 and against is 5 so all three matches can not end with draw (It is when goals for is equal to goals against) so 3 points is possible with 1 win and 2 loss.
Faraday scored only 1 goal, goal against is 4 and won 1 match it is possible only when he won by (1-0) and lost two matches with (0-2) each[ as with the combination (0-1) and (0-3) is not possible since (0-3) goal difference is 3] Since Edison won on Wednesday with (2-0) and total goals for is 5 while against is 7, so in other two game it lost with (2-4) and (1-3)
Draw is casued only with Diesel and Marconi hence they must have played with each other and the match was tie.
On Monday Diesel played with Bose, on Tuesday Diesel played with Edison while on Wednesday Diesel played with Marconi.
On Wednesday Bose must have played with Marconi
Faraday played against Edison on Wednesday and lost with (0-2)
Marconi played against Faraday on Monday while against Bose on Tuesday.
Since Rankin scored 4 goals and conceded 5 goals result of Bose and Rankin (3-1) similarly result of Rankin and Edison (3 – 1)
Now we can conclude that Bose sadan won against Diesel and Marconi with (4-2) and (4-2) Diesel won against Edison with (4-2)
So matches on Monday:
So final result
Number of points are as follows: Bose (3 + 3 + 3 = 9), Diesel (0 + 3 + 1 = 4), Edison (0 + 0 + 3 = 3), Faraday (0 + 3 + 0 = 3), Marconi (3 + 0 + 1 = 4), and Rankin (3 + 0 + 0 = 3)
Out of 9 matches only 1 match end up with tie so total number of points is 8 × 3 + 2 = 26
