A survey was conducted to know the hobby of 220 students of class IX. Out of which130 students informed about their hobby as rock climbing and 180 students informed about their hobby as sky watching. There are 110 students who follow both the hobbies. Then how many students do not have any of the two hobbies? How many of them follow the hobby of rock climbing only? How many students follow the hobby of sky watching only?

Given: n(A) = 130, n(B) = 180 and n (A ∩ B) = x = 110

Total number of students = 220

n(A) = number of students whose hobby is rock climbing

n(B) = number of students whose hobby is sky watching

n (A ∩ B) = number of students whose hobby is both

n (A ∪ B) = number of students whose hobby is either rock climbing or sky watching

As we know, n (A ∪ B) = n(A) + n(B) - n (A ∩ B)

⇒ n (A ∪ B) = 130 + 180 - 110

⇒ n (A ∪ B) = 310 - 110

⇒ n (A ∪ B) = 200

Then,

(i) The number of students who do not have any of the two hobbies

= 220– 200

= 20

(ii) The number of students whose hobby is rock climbing

= 130– 110

= 20

(iii) The number of students whose hobby is sky watching

= 180– 110

= 70