IBPS PO Quantitative Aptitude: Set Theory and Venn Diagrams questions with solutions

Q1. The information is about the total people who like three different games i.e. volleyball, chess and cricket. The people who like only volleyball is (x+10) and people who like only chess is 15 less than that of Volleyball. People who like only cricket is 28. Average number of people who like only one game is 21. People who like all the games together is 50. The ratio of people who like volleyball and chess together and chess and cricket together is 1:2. Total people who like chess is 96. The ratio of male and female who like chess is 7:5, then females who like chess is what percentage more/less than the people who like all the games together.

1. 20%
2. 10%
3. 90%
4. 80%

Answer: 20%

Average of only-one-game = 21 → (x+10)+(x-5)+28 = 63 → 2x+33=63 → x=15. Only volleyball=25, only chess=10, only cricket=28. Let V∩C only=k, C∩Cr only=2k (ratio 1:2). Total chess = 10+k+2k+50 = 60+3k = 96 → k=12. Total chess = 96. Females = 5/12×96=40. All three = 50. Females are 10 less than all three → (50-40)/50×100 = 20% less.