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Out of 800 boys in a school, 224 played cricket, 240 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey; 80 played cricket and basketball and 40 played cricket and hockey; 24 played all the three games. The number of boys who did not play any game is
  • a)
    128
  • b)
    216
  • c)
    240
  • d)
    160
Correct answer is option 'D'. Can you explain this answer?
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Out of 800 boys in a school, 224 played cricket, 240 played hockey and...
Calculation:
- Let's calculate the total number of boys who played at least one game:
- Total boys who played cricket = 224
- Total boys who played hockey = 240
- Total boys who played basketball = 336
- Total boys who played both basketball and hockey = 64
- Total boys who played cricket and basketball = 80
- Total boys who played cricket and hockey = 40
- Total boys who played all three games = 24
Applying the principle of inclusion-exclusion:
- Total boys who played at least one game = Total cricket players + Total hockey players + Total basketball players
- (Total cricket players + Total hockey players + Total basketball players) - (Total players in two games) + (Total players in all three games)
- (224 + 240 + 336) - (64 + 80 + 40) + 24
- 800 - 184 + 24
- 640
Calculating the number of boys who did not play any game:
- Number of boys who did not play any game = Total boys - Total boys who played at least one game
- 800 - 640
- 160
Therefore, the number of boys who did not play any game is 160.
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Out of 800 boys in a school, 224 played cricket, 240 played hockey and...
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Out of 800 boys in a school, 224 played cricket, 240 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey; 80 played cricket and basketball and 40 played cricket and hockey; 24 played all the three games. The number of boys who did not play any game isa)128b)216c)240d)160Correct answer is option 'D'. Can you explain this answer?
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