Question

In a group of 800 people, 550 can speak Hindi and 450 can speak English. How many can speak both Hindi and English?

Answer 1

Hint: First consider the number of people who speak both as x. Then find a number of people who speak English and Hindi only. Now find the total number of students in terms of x and then equate it with 800 to get the desired result.

Complete step-by-step answer:

In the question there is a group of 800 people out of which some know either Hindi or English. So, it is given that 500 speak Hindi and 450 speak English. So, there will be some people who know both of the languages and how to speak them.

Let’s suppose that number of people who speak Hindi is represented as $n\left( H \right)$ while those who speak in English be represented by $n\left( E \right)$ and people who can speak both can be expressed as $n\left( H\cap E \right)$ .

So, we can represent data as

$n\left( H \right)=550$

$n\left( E \right)=450$

Let $n\left( H\cap E \right)$ be equal to x.

So, $n\left( Honly \right)$will be the number of people who only know how to speak Hindi which is $\left( 500-x \right)$.

For $n\left( Eonly \right)$ there will be a number of people who only know how to speak English which is $\left( 450-x \right)$.

And the number of people who speak both the languages is x.

As we know, the total number of people is 800.

So, we can say that 800 people consists of people who only know how to speak English or Hindi in both Hindi and English.

Let’s first find out total number of people in terms of x so we can say that,

Total number of people $=$ number of people who knows English only + number of people who knows Hindi only + number of people who knows both

$=450-x+550-x+x$

So, the total number of people is $1000-x$. We know the total number of people is 800.
So, we can say

$1000-x=800$

Here, x is 200.

So, 200 people can speak both English and Hindi.

Note: Students generally have confusion between \[n\left( E \right)\] and \[n\left( Eonly \right)\] as \[n\left( E \right)\] also represents people who knows language other than English while \[n\left( Eonly \right)\] only represents those who only knows English.