Directions: Read the following information carefully and answer the question given below-
In a stadium, each player plays either tennis or badminton, but not both. Each of them plays in either the junior or senior category. It is also known that:
(i) The ratio of the number of male players to the number of female players is 3: 2.
(ii) 50% of the players who play badminton are male.
(iii) The total number of players who play tennis is 1250.
(iv) 80% of the badminton players play for the junior team.
(v) All the players who play tennis are male.
(vi) 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.
(vii) The number of female players who play badminton for the junior team is 2000.
What percent of the total players play for junior team?
  • a)
    72%
  • b)
    73.33%
  • c)
    76%
  • d)
    80%
  • e)
    66.67%
Correct answer is option 'C'. Can you explain this answer?

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Answers

EduRev CAT
Jan 19, 2022
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%

Let's construct a table and fill in the valuesThe 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 = 4:1We 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 = 4:1From the table, junior badminton players = 4B + 2000, so number of senior badminton players = B + 500Senior male badminton players = B + 500 - AAlso, junior male tennis players = 1250 - AAdding 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 = 4750Required percentage =4750 / 6250 x 100 = 76%
Let's construct a table and fill in the valuesThe 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 = 4:1We 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 = 4:1From the table, junior badminton players = 4B + 2000, so number of senior badminton players = B + 500Senior male badminton players = B + 500 - AAlso, junior male tennis players = 1250 - AAdding 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 = 4750Required percentage =4750 / 6250 x 100 = 76%