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In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both cricket and football. The rest of them play all three sports. What is percentage of people who play at least two sports?
  • a)
    23.30
  • b)
    50.00
  • c)
    28.00
  • d)
    25.00
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In a sports academy of 300 people, 105 play only cricket, 70 play only...

Total = 300 C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 – (295) = 5
% of people playing at least 25 sports
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Most Upvoted Answer
In a sports academy of 300 people, 105 play only cricket, 70 play only...
To solve this question, we can use the principle of inclusion-exclusion. Let's break down the given information step by step:

Total number of people in the sports academy = 300

Players who play only cricket = 105
Players who play only hockey = 70
Players who play only football = 50

Players who play both cricket and hockey = 25
Players who play both hockey and football = 15
Players who play both cricket and football = 30

Let's calculate the number of people who play at least two sports using the principle of inclusion-exclusion:

1. Calculate the total number of people who play only one sport:
Total = Players who play only cricket + Players who play only hockey + Players who play only football
Total = 105 + 70 + 50
Total = 225

2. Calculate the number of people who play two sports:
Players who play both cricket and hockey + Players who play both hockey and football + Players who play both cricket and football
25 + 15 + 30 = 70

3. Calculate the number of people who play all three sports:
Total number of people - (Total number of people who play only one sport + Number of people who play two sports)
300 - (225 + 70) = 5

4. Calculate the number of people who play at least two sports:
Number of people who play two sports + Number of people who play all three sports
70 + 5 = 75

Now, let's calculate the percentage of people who play at least two sports:

Percentage = (Number of people who play at least two sports / Total number of people) * 100
Percentage = (75 / 300) * 100
Percentage = 25%

Therefore, the correct answer is option D) 25.00%.
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In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both cricket and football. The rest of them play all three sports. What is percentage of people who play at least two sports?a)23.30b)50.00c)28.00d)25.00Correct answer is option 'D'. Can you explain this answer?
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