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The information is about the total people who like three different games: volleyball, chess, and cricket. The number of people who like only volleyball is (x + 10), and the number of people who like only chess is 15 less than that of volleyball. The number of people who like only cricket is 28. The average number of people who like only one game is 21. The number of people who like all three games is 50. The ratio of people who like volleyball and chess together to those who like chess and cricket together is 1:2. The total number of people who like chess is 96. The number of people who like only volleyball and cricket together is double the number of people who like only cricket. Find the number of people who like volleyball.
- 120
- 125
- 143
- 110
Correct answer: 143
Solution
The average of the three 'only one game' groups is 21, so their total is 63. Let only volleyball = x + 10, only chess = x - 5, and only cricket = 28; then (x + 10) + (x - 5) + 28 = 63, giving x = 15 and only volleyball = 25, only chess = 10. Using the remaining conditions with the total chess count 96 and the given pairwise ratio leads to the volleyball total as 143.
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