Correct Answer - Option 3 : 16
Given:
Total boys = 37
Numbers of boys who like football = 21
Number of boys who like football and cricket = 13
Calculation:
Total number of boys, n(A∪B) = 37
Number of boys like both football and cricket, n(A∩B) = 13
Number of boys like football, n(A) = 21
Let, number of boys like only cricket, n(B) = x
According to set theory formula,
⇒ n(A∪B) = n(A) + n(B) – n(A∩B)
⇒ 37 = 21 + x – 13
⇒ x = 50 – 21
⇒ x = 29
Number of boys like cricket 29
⇒ Number of boys like only cricket = (29 - 13) = 16
∴ 16 boys like only cricket.