Question:
In a group of people:
• 70 play only Hockey.
• 100 play only Football.
• 30 play both Hockey and Football.
• 150 play neither game.
What percentage of the people play Hockey?
In a group of people:
• 70 play only Hockey.
• 100 play only Football.
• 30 play both Hockey and Football.
• 150 play neither game.
What percentage of the people play Hockey?
• 70 play only Hockey.
• 100 play only Football.
• 30 play both Hockey and Football.
• 150 play neither game.
What percentage of the people play Hockey?
Show Hint
While finding the number of people in a set, always include those who belong exclusively to the set as well as those belonging to the intersection.
Updated On: Jun 11, 2026
- \(28.57\%\)
- \(46.6\%\)
- \(66.6\%\)
- \(20\%\)
Show Solution
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The Correct Option is A
Solution and Explanation
Concept:
For two-set problems, first calculate the total number of people and then determine the number belonging to the required category.
People playing Hockey include:
• Only Hockey players
• Players playing both Hockey and Football
Step 1: Find total number of people. \[ 70+100+30+150=350 \] Hence total people \[ =350 \]
Step 2: Find number of Hockey players. Hockey players \[ =70+30 \] \[ =100 \]
Step 3: Calculate percentage. \[ \text{Percentage} = \frac{100}{350}\times100 \] \[ = 28.57\% \] Therefore, \[ \boxed{28.57\%} \] \[ \boxed{\text{Answer = (A)}} \]
• Only Hockey players
• Players playing both Hockey and Football
Step 1: Find total number of people. \[ 70+100+30+150=350 \] Hence total people \[ =350 \]
Step 2: Find number of Hockey players. Hockey players \[ =70+30 \] \[ =100 \]
Step 3: Calculate percentage. \[ \text{Percentage} = \frac{100}{350}\times100 \] \[ = 28.57\% \] Therefore, \[ \boxed{28.57\%} \] \[ \boxed{\text{Answer = (A)}} \]
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