Solution:

Let us first calculate the total number of matches that will be placed:
9C2 * 2
= 9! / (2!7!) * 2
= 8 * 9
= 72
Therefore, every team will play 16 matches.

Let us now glance over the cases that are possible.

Case 1:
Let us say that Team A, Team B and Team C wins 14 matches each (they lose 1 match each from the other two teams), then the Team D can win only (16 - 3 * 2) = 10 matches.

Case 2:
Suppose that, the top 4 teams win 13 matches each.
Team A will win 13 matches and will lose 3 matches from Team B, Team C and Team D.
Team B will win 13 matches and will lose 3 matches from Team A, Team C and Team D.
Team C will win 13 matches and will lose 3 matches from Team A, Team B and Team D.
Team D will win 13 matches and will lose 3 matches from Team A, Team B and Team C.

If this case actually happens, then the Team E will be able to win 8 matches at maximum as Team A, Team B, Team C and Team D will win all the matches played by E.

Case 3:
Suppose that, the top 5 teams win 12 matches each.
Team A will win 12 matches and will lose 3 matches from Team B, Team C, Team D and Team E.
Team B will win 12 matches and will lose 3 matches from Team A, Team C, Team D and Team E.
Team C will win 12 matches and will lose 3 matches from Team A, Team B, Team D and Team E.
Team D will win 12 matches and will lose 3 matches from Team A, Team B, Team C and Team E.
Team E will win 12 matches and will lose 3 matches from Team A, Team B, Team C and Team D.

If this case actually happens, Team E will win 12 matches but it still won't be able to get into the playoffs assuming that it has the lowest run rate among all.

This implies that from case 2, it is evident that a team must win 13 matches at the least to confirm its position in the playoffs.

Solution:

2/5

Explanation:
This problem can be solved with different approaches. Let us not go into the complicated generic stuff to avoid confusion and try to solve it with simpler means.

Let us find the results separately. There can be 4 different results that give the sum of 5 and there can be 6 different results that give the sum of 7.

Thus, the probability that we get the sum of 4 before the sum of 7 will be:
4/(4+6) = 4/10 = 2/5.

Solution:

130

Explanation:
(1*1*1)+1 = 02
(2*2*2)+2 = 10
(3*3*3)+3 = 30
(4*4*4)+4 = 68
(5*5*5)+5 = 130

Solution:

2 Hours

Lets consider the garden breadth as "B" and its length as "2B". The man starts from one end of the breadth, while the snake starts from one end of the length.

The man covers 60 cm in an hour, and the snake covers 30 cm in an hour.

To find the time "T" when the man catches the snake, we equate the distances they both cover.

Man distance: 60T (60 cm/hour * T hours)
Snake distance: 30T (30 cm/hour * T hours)

Since the man catches the snake when they meet at the same point, the distance covered by both will be equal.

Equation: 60T = 30T

Solving for "T":
60T - 30T = 0
30T = 0
T = 2

So, the man catches the snake after 2 hours.

Solution:

36

Solution:

288/61 hours (4 hours, 43 minutes and 17 seconds approx)

Explanation:
In 1 hour, the ratio of swimming pool filled by pipes:
1st pipe: 1/48
2nd pipe: 1/72
3rd pipe: 1/96
4th pipe: 1/6

All togther
1/48 + 1/72 + 1/96 + 1/6
=> (6+4+3+48) / 288 = 61/288.
=> 288/61 hours,

which is 4 hours 43 minutes and about 17 seconds.

Solution:

28745

Explanation

New Number = (Last Number +1 ) * 9
and Then New Number = (Last Number - 1 ) * 8 and so on.

i.e
1
(1+1) * 9 = 18
(18-1) * 8 = 136
(136+1) * 7 = 959
(959-1) * 6 = 5748
(5748+1) * 5 = 28745
(28745-1) * 4 = 114976
(114976+1) * 3 = 344931

Solution:

120 km

Solution:

450

Explanation:
II - IV + IX = 200
=> VII = 200

VI + I - V = 100
=> II =100

II - VI + VII = 150
=> III = 150

Therefore,
VII + II + III = 200 + 100 + 150 = 450

Solution:

The solution is:
547809 + 087549 + 780954 = 1416312