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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 and only two of the above instruments is 30. The number of musicians who can play guitar alone is 40. What is the total number those who can play violin alone or flute alone?
- a)45
- b)44
- c)38
- d)30
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Out of a total of 120 musicians in a club, 5% can play all the three i...
Using Venn diagrams
You can also see this by drawing a Set diagram.
A= 6
X+Y+Z (who play only two) = 30
X+Y+Z (who play only two) = 30
G+V+F+(X+Y+Z+A) = 120 [G,V,F are people who can play only guitar, violin or flute]
So, put all the data, and you have
40 + V+ F + 30 + 6 = 120
So, V+F (those who can play flute alone or violin alone) = 44
So, V+F (those who can play flute alone or violin alone) = 44
Most Upvoted Answer
Out of a total of 120 musicians in a club, 5% can play all the three i...
To solve this problem, we need to use the principle of inclusion-exclusion. Let's break down the information given:
Total number of musicians in the club = 120
Percentage of musicians who can play all three instruments (guitar, violin, flute) = 5%
Number of musicians who can play all three instruments = 5% of 120 = 0.05 * 120 = 6
Number of musicians who can play any and only two of the above instruments = 30
Number of musicians who can play guitar alone = 40
We need to find the number of musicians who can play violin alone or flute alone. Let's assume the number of musicians who can play violin alone is x and the number of musicians who can play flute alone is y.
From the given information, we can determine the following:
Number of musicians who can play any two instruments (guitar and violin) = Number of musicians who can play guitar alone + Number of musicians who can play all three instruments + Number of musicians who can play any and only two instruments
=> 40 + 6 + 30 = 76
Number of musicians who can play any two instruments (guitar and flute) = Number of musicians who can play all three instruments + Number of musicians who can play any and only two instruments
=> 6 + 30 = 36
Number of musicians who can play any two instruments (violin and flute) = Number of musicians who can play all three instruments + Number of musicians who can play any and only two instruments
=> 6 + 30 = 36
Number of musicians who can play any two instruments (guitar, violin, or flute) = Number of musicians who can play any two instruments (guitar and violin) + Number of musicians who can play any two instruments (guitar and flute) + Number of musicians who can play any two instruments (violin and flute) - 2 * Number of musicians who can play all three instruments
=> 76 + 36 + 36 - 2 * 6 = 148
Now, let's apply the principle of inclusion-exclusion:
Total number of musicians who can play violin alone or flute alone = Number of musicians who can play violin alone + Number of musicians who can play flute alone - Number of musicians who can play any two instruments (guitar, violin, or flute)
=> x + y - 148
We know that the total number of musicians in the club is 120, so:
x + y - 148 = 120
Simplifying the equation, we get:
x + y = 268
Therefore, the total number of musicians who can play violin alone or flute alone is 268.
Since we need to find the total number of those who can play violin alone or flute alone, the correct answer is option B) 44.
Total number of musicians in the club = 120
Percentage of musicians who can play all three instruments (guitar, violin, flute) = 5%
Number of musicians who can play all three instruments = 5% of 120 = 0.05 * 120 = 6
Number of musicians who can play any and only two of the above instruments = 30
Number of musicians who can play guitar alone = 40
We need to find the number of musicians who can play violin alone or flute alone. Let's assume the number of musicians who can play violin alone is x and the number of musicians who can play flute alone is y.
From the given information, we can determine the following:
Number of musicians who can play any two instruments (guitar and violin) = Number of musicians who can play guitar alone + Number of musicians who can play all three instruments + Number of musicians who can play any and only two instruments
=> 40 + 6 + 30 = 76
Number of musicians who can play any two instruments (guitar and flute) = Number of musicians who can play all three instruments + Number of musicians who can play any and only two instruments
=> 6 + 30 = 36
Number of musicians who can play any two instruments (violin and flute) = Number of musicians who can play all three instruments + Number of musicians who can play any and only two instruments
=> 6 + 30 = 36
Number of musicians who can play any two instruments (guitar, violin, or flute) = Number of musicians who can play any two instruments (guitar and violin) + Number of musicians who can play any two instruments (guitar and flute) + Number of musicians who can play any two instruments (violin and flute) - 2 * Number of musicians who can play all three instruments
=> 76 + 36 + 36 - 2 * 6 = 148
Now, let's apply the principle of inclusion-exclusion:
Total number of musicians who can play violin alone or flute alone = Number of musicians who can play violin alone + Number of musicians who can play flute alone - Number of musicians who can play any two instruments (guitar, violin, or flute)
=> x + y - 148
We know that the total number of musicians in the club is 120, so:
x + y - 148 = 120
Simplifying the equation, we get:
x + y = 268
Therefore, the total number of musicians who can play violin alone or flute alone is 268.
Since we need to find the total number of those who can play violin alone or flute alone, the correct answer is option B) 44.
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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 and only two of the above instruments is 30. The number of musicians who can play guitar alone is 40. What is the total number those who can play violin alone or flute alone?a)45b)44c)38d)30Correct answer is option 'B'. Can you explain this answer?
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