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
None of the above/More than one of the above
Incorrect AnswerExplanation:
24
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:
As per the details,
Students playing neither 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%
Thus, the number of students who play only chess = 30% of 80
⇒ (30/100) x 80 = 24
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By: Parvesh Mehta