Out of a total of 120 musicians in a club, 5% can play all the three instruments, guitar, violin and flute. It so happens that the number of musicians who can play any two and only two of the above instruments is 30. The number of musicians who can play the guitar alone is 40. What is the total number of those who can play violin alone or flute alone ?
(a) 45
(b) 44
(c) 38
(d) 30
Answers
Answered by
19
By use of Venn Diagrams we get,
|A∪B∪ C| = |A| + |B| + |C| −|A ∩ B|−|A ∩ C| − |B ∩ C| + |A ∩ B ∩ C|.
We have,
Total No of musicians, |A∪B∪ C| = 120
5% can play all the three instruments, guitar, violin and flute, |A ∩ B ∩ C| = 5% of 120= 6.
No of people playing two instruments = 30
No. of people playing guitar alone is 40, so, |A| = 40
|A∪B∪ C| = |A| + |B| + |C| −|A ∩ B|−|A ∩ C| − |B ∩ C| + |A ∩ B ∩ C|.
putting values, we get
120-(40-6-30) = 44.
so, 44 can play violin alone or flute alone
|A∪B∪ C| = |A| + |B| + |C| −|A ∩ B|−|A ∩ C| − |B ∩ C| + |A ∩ B ∩ C|.
We have,
Total No of musicians, |A∪B∪ C| = 120
5% can play all the three instruments, guitar, violin and flute, |A ∩ B ∩ C| = 5% of 120= 6.
No of people playing two instruments = 30
No. of people playing guitar alone is 40, so, |A| = 40
|A∪B∪ C| = |A| + |B| + |C| −|A ∩ B|−|A ∩ C| − |B ∩ C| + |A ∩ B ∩ C|.
putting values, we get
120-(40-6-30) = 44.
so, 44 can play violin alone or flute alone
Answered by
0
Answer:
Explanation:By using venn diagram this type of question were solved.
Similar questions