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 th

examrobotsa's picture

Submitted by examrobotsa on

Q: 148 (IAS/1995)
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 ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,5,4,2,5,2,0

keywords: 

{'musicians': [0, 1, 0, 0], 'violin': [0, 0, 1, 0], 'instruments': [2, 1, 2, 2], 'flute': [0, 1, 1, 0], 'guitar': [0, 1, 0, 0], 'total number': [0, 0, 3, 0], 'above instruments': [0, 1, 0, 0], 'club': [0, 2, 1, 1], 'number': [0, 0, 0, 2], 'total': [0, 1, 1, 1]}

The number of musicians who can play all three instruments is 5% of 120, which is 6. The number of musicians who can play any two instruments is given as 30. The musicians who can play the guitar alone are 40. So, to find out the number of musicians who can play either the violin alone or the flute alone, we need to subtract the number of musicians who can play more than one instrument and those who can play the guitar alone from the total number of musicians.

Calculation: 120 (total number of musicians) - 6 (musicians who can play all three instruments) - 30 (musicians who can play any two instruments) - 40 (musicians who can play the guitar alone) = 44

So, option 2 is the correct answer. The remaining musicians either play the violin alone or the flute alone, hence number 44. Options 1, 3, and 4 are incorrect as their values do not match with the result obtained in our calculations.