Question

In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find: How many can speak Hindi only.

Answer 1

Hint: Let’s go into the solution by assigning the persons in the form of set and then apply the properties of set i.e. $n(A \cup B) = n(A) + n(B) - n(A \cap B)$. For finding the terms asked in question.

Let the person who can speak Hindi are in set A i.e. $n(A) = 750$
And Let the person who can speak English are in set B i.e. $n(B) = 460$
And here it is given that a group of 950 persons which means they speak either English or Hindi
i.e. $n(A \cup B) = 950$.

Now for finding how many speaks only Hindi we have to first find out who speaks Hindi and English both.
i.e. $n(A \cap B)$.
Now by applying the properties of set,
\[
  n(A \cup B) = n(A) + n(B) - n(A \cap B) \\
  950 = 750 + 460 - n(A \cap B) \\
  n(A \cap B) = 1210 - 950 \\
  \therefore n(A \cap B) = 260 \\
 \]
There are 260 people who speak Hindi and English both.

Now for finding the person who speaks only Hindi we have to subtract the person who speaks Hindi and English both from the person who speaks Hindi. I.e. 750-260=490

Therefore the required answer is 490.

Note: Whenever we face such a type of question the key concept for solving the question is first we have to find the person who can speak English and Hindi both. Then after that we subtract the person who speaks English and Hindi both from the person who speaks Hindi to find out the number of people who speak only Hindi.