three groups named A, B and C in a troupe. In group A, there are 40% singers of the total number of singers and 50% dancer of the total number of dancers. In group B, singers are 30% of the total number of singers and dancers are 30% of the total number of dancers. Group C has 30% singers of the total number of singers and 20% dancers of total number of dancers. 8 dancers and 11 singers are involved in group A and B both. 7 dancers and 8 singers are involved in group B and C both. 5 dancers and 7 singers are involved in group A and C both. 3 dancers and 4 singers are involved in all the groups.
1. What percentage of artists are involved in any two groups at a time?
1) 18.89%
2) 15.89%
3) 16.19%
4) 17.69%
4) 17.69%
5) None of these
2. What is the ratio of the total dancers to singers involved in either group A or group B but not in both?
1) 48: 49
2. What is the ratio of the total dancers to singers involved in either group A or group B but not in both?
1) 48: 49
2) 47 : 49
3) 53 : 49
4) 53:48
4) 53:48
5) None of these
3. By what per cent is the number of dancers involved in group A only more than the number of singers involved in group B only ?
1) 45.86%
3. By what per cent is the number of dancers involved in group A only more than the number of singers involved in group B only ?
1) 45.86%
2) 42.86%
3) 49.86%
4) 69.86%
4) 69.86%
5) None of these
4.The number of singers involved either in group 'A' or in group 'B' but not in both is by what per cent is more than the number of dancers involved either in group 'A' or in group 'C' but not in both ?
1) 18.67%
4.The number of singers involved either in group 'A' or in group 'B' but not in both is by what per cent is more than the number of dancers involved either in group 'A' or in group 'C' but not in both ?
1) 18.67%
2) 16.67%
3) 20.67%
4) 21.67%
4) 21.67%
5) None of these
5. The total number of artist involved in all the groups is what percent of the artists involved in both group B and C?
1) 45.67%
5. The total number of artist involved in all the groups is what percent of the artists involved in both group B and C?
1) 45.67%
2) 48.67%
3) 46.67%
4) 42.67%
3) 46.67%
4) 42.67%
5) None of these
Answer:
Dancer= 6/13 x 260=120
13

Dancer  Singer  
Group A  60  56 
Group B  36  42 
Group C  24  42 
Group A and B (A ∩ B)  8  11 
Group B and C (B ∩ C)  7  8 
Group C and A (C ∩ A)  5  7 
Group A,B & C (A ∩ B ∩C)  3  4 
1. 4; Required percentage = x 100 = x 100 = 17.69% 2. 1; Required Ratio = (60+36) : (56+42) = 96:98 = 48:49 3. 2; Required Percentage = x 100 = x 100 = 42.86% 4. 2; Required Percentage = x 100 = x 100 = 16.67% 5. 3; Required Percentage = x 100 = 46.67% 
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