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There are 75 students in a class, they all play at least one of the instruments namely violin, guitar, and harmonium. Further it is known that, 15 students play all the three instruments. 20 students play both guitar and violin, 30 students play both guitar and harmonium and 25 students play both violin and harmonium. A total of 50 students can play harmonium and a total of 45 students play violin. What is the number of students who can play only guitar?

There are 75 students in a class, they all play at least one of the instruments namely violin, guitar, and harmonium. Further it is known that, 15 students play all the three instruments. 20 students play both guitar and violin, 30 students play both guitar and harmonium and 25 students play both violin and harmonium. A total of 50 students can play harmonium and a total of 45 students play violin. What is the number of students who can play only guitar? Correct Answer 5

1) 15 students play all the three instruments.

2) 20 students play both guitar and violin it means (20 – 15) = 5 play only guitar and violin

3) 30 students play both guitar and harmonium it means (30 – 15) = 15 play only guitar and harmonium

4) 25 students play both violin and harmonium it means (25 – 15) = 10 play only violin and harmonium

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Therefore, students who play only violin = 45 – (5 + 15 + 10) = 45 – 30 = 15

Therefore, students who play only harmonium = 50 – (15 + 15 + 10) = 50 – 40 = 10

Hence, the students who play only guitar = Total students – (total students who play harmonium + students who play only guitar and violin + students who play only violin)

OR,

Hence, the students who play only guitar = Total students – (total students who play violin + students who play only guitar and harmonium + students who play only harmonium)

In both the cases we get same result,

Hence, the students who plays only guitar = 75 – (45 + 15 + 10) = 75 – 70 = 5.

Hence, 5 students play only guitar.

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