In a school, all students play either football or cricket or both. If 250 play football, 300 play cricket and 120 play both the games, then the total number of students in the school is ____.

550

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430

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400

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500

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Solution

The correct option is B
430

If the sets F and C stand for the sets of students that play football and cricket respectively, then by question

$n (F) = 250, n (C) = 300$ and $n (F \cap C) = 120.$

$But, n (F \cup C) = n (F) + n (C) - n (F \cap C) .$

$= 250 + 300 - 120$

$= 430$

Thus, the total number of students in the school is 430.

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In a school, all students play either football or cricket or both. If 250 play football, 300 play cricket and 120 play both the games, then the total number of students in the school is ____.

The correct option is B 430 If the sets F and C stand for the sets of students that play football and cricket respectively, then by question n(F)=250, n(C)=300 and n(F∩C)=120. But, n(F∪C)=n(F)+n(C)−n(F∩C). =250+300–120 =430 Thus, the total number of students in the school is 430.