Question

In a certain group of 200 persons, 110 can speak Nepali, 85 can speak Maithili and 60 can speak both the languages.

Find,
(i) how many of them can talk in either of these languages?
(ii) how many of them can talk in neither of these languages?​​

Answer 1

85 - 60 = 25 people speak Maithili only

110 - 60 = 50 people speak Nepali only

(i) 25 + 50 + 60 = 135 people speak either language

(ii) 200 - 135 = 65 people can speak neither language

Answer 2

i. 135 people

ii. 65 people

Explanation:

Let n(U) be a group of people, n(N) be people who talk Nepali, n(M) be People who talk Maithili.

To solve this problem, we can use the principle of set theory and the Inclusion-Exclusion principle. We are given the following information:

• n(U) = 200 (the total number of people in the group).
• n(N) = 110 (the number of people who can speak Nepali).
• n(M) = 85 (the number of people who can speak Maithili).
• n(N ∩ M) = 60 (the number of people who can speak both Nepali and Maithili).

Now, let's find the answers to questions:

Part (i)

To find the number of people who can speak either Nepali or Maithili (or both), you can use the principle of inclusion-exclusion. The formula for this is:

n(N ∪ M) = n(N) + n(M) - n(N ∩ M)

Substitute the given values:

n(N ∪ M) = 110 + 85 - 60

n(N ∪ M) = 135

So, 135 people can speak either Nepali, Maithili, or both.

Part (ii)

To find the number of people who can't speak either Nepali or Maithili, you'll subtract the number of people who can speak at least one of the languages from the total group.

n(N or M) = n(U) - n(N ∪ M)

Substitute the values:

n(N or M) = 200 - 135

n(N or M) = 65

So, 65 people in the group can't speak either Nepali or Maithili.