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​

Answer 1

Answer:

50 people can speak both languages

Answer 2

50 People

Let H be the set of the people who speak Hindi

Let E be the set of the people who speak English

n(H U E) = 400

n(H) = 250

n(E) = 200

To Find:

The number of people who can speak both Hindi and English n(H ⋂ E)

Calculating:

The formula to find the union of sets is:

n(H U E) = n(H) + n(E) - n(H ⋂ E)

Taking n(H ⋂ E) to the other side of the formula we get:

n(H ⋂E) = n(H) + n(E) - n(H U E)

Substituting all the values known to us in this formula we get:

n(H ⋂ E) = 250 + 200 - 400

n(H ⋂ E) = 450 - 400

n(H ⋂ E) = 50

Therefore, 50 People can speak both Hindi and English .