Question

In a group of 850 persons, 600 can speak Hindi and 340 can speak Tamil.
Find

(i) How may can speak both Hindi and Tamil?

(ii) How many can speak Hindi only?

(iii) How many can speak Tamil only?

Answer 1

Let A = set of persons who can speak Hindi
and B = set of persons who can speak Tamil

$\therefore n\left(A\right)=600,n\left(B\right)=340andn(A\cup B)=850$

(i) Set of persons who can speak both Hindi and Tamil = $(A\cap B)$.

Now, $n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cup B)=(600+340-850)=90$

Thus, 90 persons can speak both Hindi and Tamil.

(ii) Set of persons who can speak Hindi
only = (A-B).
Now, $n(A-B)+n(A\cap B)=n\left(A\right)$
$\Rightarrow n(A-B)=n\left(A\right)-n(A\cap B)=(600-90)=510$
Thus, 510 persons can speak Hindi only.

(iii) Set of persons who can speak Tamil only = (B-A)

Now, $n(B-A)+n(A\cap B)=n\left(B\right)$

$\Rightarrow n(B-A)=n\left(B\right)-n(A\cap B)=(340-90)=250$

Hence, 250 persons can speak Tamil only.