A, B, C and D were the members of a team. The average runs of the team...
Let the average runs of the team before adding E be x.
Total runs scored by A and B = 13x + 12x = 25x
Total runs scored by C and D = 2x (since average runs decreases by 2 when E is added)
Total runs scored by the team before adding E = 25x + 2x = 27x
After adding E, the average runs of the team decreases by 2. So, the new average runs = x - 2.
Total runs scored by the team after adding E = (x - 2) * 5
Since E scored 45 runs, we can write the equation:
(x - 2) * 5 = 45
x - 2 = 9
x = 11
So, the average runs before adding E = 11.
Total runs scored by the team before adding E = 27x = 27 * 11 = 297
Now, let's find the individual runs scored by each player.
Since no player scored less than E or more than 65 runs, we can conclude that A scored 65 runs and B scored 65 - 13 = 52 runs.
Let's assume that C scored y runs. Since C scored more than A, y > 65. Also, since y is a natural number, the minimum value of y is 66.
Total runs scored by the team = 65 + 52 + y + 2x = 297
117 + y + 22 = 297
y = 158
So, C scored 158 runs and D scored 297 - 65 - 52 - 158 = 22 runs.
The ratio of the runs scored by B to the average runs scored by C & D = 52 : ((158 + 22)/2) = 52 : 90 = 4 : 5
Therefore, the correct answer is A: 4:5.