Let's construct a table and fill in the values
The number of female players who play badminton for the senior team is equal to the total number of players who play tennis for the senior team.
Let this number be A.
80% of the badminton players play for the junior team. This implies 20% of the badminton players play for the senior team.
Hence, ratio of junior and senior badminton players = 4:1
We know, there are 2000 junior female badminton players. So, the number of junior male badminton players should be a multiple of 4. Let this number be 4B.
As calculated above, ratio of junior and senior badminton players = 4:1
From the table, junior badminton players = 4B + 2000, so number of senior badminton players = B + 500
Senior male badminton players = B + 500 - A
Also, junior male tennis players = 1250 - A
Adding the values in the table:
The ratio of the number of male players to the number of female players is 3: 2.
(4B + 1250 - A + 500 + B) : (2000 + A) = 3:2
⇒ 2(1750 + 5B - A) = 3(2000 + A)
⇒ 3500 + 10B - 2A = 6000 + 3A
⇒ 2B - A = 500 (i)
50% of the players who play badminton are male.
4B + 500 + B - A = 2000 + A
⇒ 5B - 2A = 1500 (ii)
Solving (i) and (ii), we get A = 500, B = 500.
Substituting the values in the table,
The number of players who play for junior team = 2750 + 2000 = 4750
Required percentage =4750 / 6250 x 100 = 76%