related.our chat very important quest

[Aditya Sharma]

Sir as we talked on that topic where in 400people where 200people
speak english and 250 speak hindi how many can speak bith languages.if
here 400 is univesal set as u told me then plz send me solutions of
this answer plz ad it very fasttt..

[chawla.kunal29]

plz see the attachment

[Dr. Atul Nischal]

Aditya,

Here is the question:

In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?


The problem with this question is that it does not rule out the fact that some people in the group speak a language other than Hindi or English. So, it is not correct to assume that n(Hindi U English) = 400. 

But, at the same time, if you do not assume this, it is impossible to find the answer. 

The question statement is incomplete or you can make the assumption and solve the problem to get the answer that NCERT has provided.

[Dr. Atul Nischal]

Aditya,

Here is the best correct solution of the problem. Let me know if you understand how the inequality is coming in.

Let A be the set of people who can speak Hindi, and B be the set of people who can speak English. Then A∪ B is the set of people who can speak at least one language, and A ∩ B is the set of people who can speak both of the languages.

We know that, if A and B are finite sets, then

n(A ∪ B) = n(A) +  n(B) – n(A ∩ B).

We are given, 250 people can speak Hindi, 200 can speak English.

Therefore, n(A) = 250, n(B) = 200, 250 ≤  n(A ∪ B ) ≤ 400.

Note: In the problem, it is not given that each of the 400 people can speak at least one of the two languages. So, n(A ∪ B ) ≠ 400.

We need to find (A ∩ B).

n(A ∩ B) = n(A) +  n(B) – n(A ∪ B)

On substituting the values n(A) = 250, n(B) = 200, we get

n(A ∩ B) = 250 + 200 – n(A ∩ B) = 450  – n(A ∩ B). 

Since 250 ≤  n(A ∪ B ) ≤ 400, we have

50  ≤  n(A ∩ B) ≤ 200

Thus, the number of people who can speak both English and Hindi is between 50 and 200.

On Thursday, 2 July 2015 16:48:47 UTC+5:30, adityash.2228 wrote: