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In a class of 80 students, 60% students play carrom, 45% play chess and 10% students neither play carrom nor chess. The number of students who play only chess is

In a class of 80 students, 60% students play carrom, 45% play chess and 10% students neither play carrom nor chess. The number of students who play only chess is Correct Answer 24

Given:

Total students = 80

Students play carrom, n(X) = 60%

Students play chess, n(Y) = 45%

Students neither play carrom nor chess, n(X ∩ Y)' = 10%

Formula used:

n(X ∪ Y) = n(X) + n(Y) - n(X ∩ Y) 

Calculation:

From the given details,

Students play either carrom nor chess, n(X ∪ Y) = 100 - 10 = 90%

n(X ∪ Y) = n(X) + n(Y) - n(X ∩ Y) 

⇒ 90% = 60% + 45% - n(X ∩ Y) 

⇒ n(X ∩ Y) = 15%

The number of students who play only chess = n(Y) - n(X ∩ Y) 

⇒ 45% - 15% = 30%

∴ The number of students who play only chess = 30% of 80

⇒ (30/100) × 80 = 24

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