UPSC Prelims 2014·CSAT·Quantitative Aptitude·Combinatorics and Probability

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?

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Last updated 23 May 2026, 3:31 pm IST
  1. A45
  2. B44Correct
  3. C38
  4. D30

Explanation

Here's a brief explanation: 1. **Musicians playing all three instruments:** 5% of 120 = (5/100) * 120 = 6 musicians. 2. **Musicians playing exactly two instruments:** Given as 30. 3. **Musicians playing guitar alone:** Given as 40. The total number of musicians (120) is the sum of those playing: * Guitar alone * Violin alone * Flute alone * Exactly two instruments * All three instruments So, 120 = (Guitar alone) + (Violin alone + Flute alone) + (Exactly two instruments) + (All three instruments). Substitute the known values: 120 = 40 + (Violin alone + Flute alone) + 30 + 6 Combine the known numbers: 120 = 76 + (Violin alone + Flute alone) Now, solve for the sum of those playing violin alone or flute alone: (Violin alone + Flute alone) = 120 - 76 (Violin alone + Flute alone) = 44 Therefore, the total number of those who can play violin alone or flute alone is 44. The final answer is B) 44.
Quantitative Aptitude: Out of a total of 120 musicians in a club, 5% can play all the three instruments, guitar, violin and flute. It so happen
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