Out of 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 or flute alone ?

Options

A. 1. 30
B. 2. 44
C. 3. 38
D. 4. 45

Answer

B

Explanation

Let circles G, Vand F represent tlie fitasnians Wavi can play Guitar, Violin and Flute respectively.
According to the question,
Total no. of musicians in a club= `n (G uu V uu F)`
`= a + b + c + d + e + f + g = 120 `

Number of musicians who can play all the three instruments
`= n(G nn V nn F) = d = 5% of 120 = 5/100 xx 120 = 6`
Number of musicians who can play any two and only two of the instruments
`[n (G nn V) + n(G nn F) + n(F nn V)] = b + e + f = 30 `
Number of musicians who can play guitar only
`= n (G) = Q = 40 `
As we know that
`n(G uu V uu F)= n(G) + n (V) + n(F) + [n(G nn V) `
`+ n(GnnF) + n(F nn V)] + n(Gnn V nn F)`.
[`because` Formula of set theory]
Putting the values, we get
`120 = 40 +n (V) +11 (F) + 30+6 `
or, `n(V) + n(F) = 44`.
Therefore, number of Musicians who can play violin alone or flute only
`= n (V) + n(F) = c + g = 44`