Question

Question 3 Single Choice

Out of a group of 30 friends, 20 visited Nepal and 27 visited Sri Lanka. If 5 friends did not visit either

Nepal or Sri Lanka, how many friends visited both Nepal and Sri Lanka?

Answer 1

Answer:

group of 30 friends.

visited nepal-20

visited Sri Lanka- 27

friends didn't visit anyplace-5

=20+27

=47

47-30=17

so 17 children visited both Nepal and Sri Lanka.

Answer 2

given a group of friends travelling Nepal and Sri Lanka, find how many visited both the places

Explanation:

1. let the set of friends who visited Sri Lanka be denoted by S and set of friends who visited Nepal be denoted by N
2. given total number of friends $=30$ and friends who did not visit any place $=5$. Then, the union of sets S and N denote the no. of friends who visited at least one place ,  $n(S$∪$N)=30-5=25$  
3. from set theory we know  $n(S$∪$N)$$=n(S)+n(N)-n$$(S$∩$N)$                                            where, n(S), n(N)  are no. of friends who visited Sri Lanka and Nepal respectively and n(S∩N) are no. of friends who visited both the places
4. from given data we get, $n(S)=27,\ n(N)=20,\ from\ point\ 2.\, n(S$∪$N)=25$  
5. putting these values in equation from point 3. we get, $n(S$∩$N)=22$   , friends visited both Nepal and Sri Lanka.