Discussion

Explanation:

Out of total students 20 like cricket and 25 like football. 
Let x be the number of students who like bot the sports.
∴ Number of students who like only cricket = 20 - x
∴ Number of students who like only football = 25 - x 
⇒ Number of students who like at least one of the sport = (20 - x) + (25 - x) + x ≤ 40
⇒ 5 ≤ x
∴ Minimum value of x = 5.

Alternately,
Let the number of students who,
like exactly 1 sport = a
like exactly 2 sports = b
like none of the 2 sports = n

⇒ a + b + n = 40   …(1)
and, a + 2b = 20 + 25 = 45   …(2)

(2) – (1)
⇒ b – n = 5
⇒ b = 5 + n

Minimum value of b = 5 when n = 0.

Hence, 5.

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