In a class of $60$ students, $45$ students like music, $50$ students like dancing, $5$ students like neither. Then the number of students in the class who like both music and dancing is

35

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40

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50

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55

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Solution

The correct option is C $40$
Total number of students in class $= 60$
Students who like music $= X + Y = 45$
Students who like dancing $= Y + Z = 50$
Students who like nothing $= 5$
Students who like both music and dancing $= Y$
We know that $X + Y + Z + 5 = 60$
$\Rightarrow 45 + Z + 5 = 60$
$\Rightarrow Z = 10$
$\Rightarrow Y = 40$
Hence, $40$ students like both music and dancing.

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In a class of 60 students, 45 students like music, 50 students like dancing, 5 students like neither. Then the number of students in the class who like both music and dancing is

The correct option is C 40Total number of students in class =60Students who like music =X+Y=45Students who like dancing =Y+Z=50Students who like nothing =5Students who like both music and dancing =YWe know that X+Y+Z+5=60⇒45+Z+5=60⇒Z=10⇒Y=40Hence, 40 students like both music and dancing.

In a class of $60$ students, $45$ students like music, $50$ students like dancing, $5$ students like neither. Then the number of students in the class who like both music and dancing is