In a group of 50 people, 35 speak Hindi, 25 speak both English and Hindi and all the people speak - Maths -

Question

In a group of 50 people, 35 speak Hindi, 25 speak both English
and Hindi and all the people speak at least one of the two
languages How many people speak only English and not Hindi? How
many people speak English?

shanul.singh · Accepted Answer

n(A U B )= people who speak in
either hindi and english

Given people speak atleast one
of the languages

n(A U B) = 50

n(A ^ B) =people who speak in
both the languages = 25

n(A) = people who speak in
english = x

n(B) = people who speak in hindi
= 35

We have n(A U B) = n(A)+n(B) -
n(A ^ B)

= 50 = x + 35-25

= x = 50-10 = 40

thefore n(A)= 40 (ie no of
people who speak in english)

People who speak english not
hindi=40-25

=15

In a group of 50 people, 35 speak Hindi, 25 speak both English and Hindi and all the people speak at least one of the two languages. How many people speak only English and not Hindi? How many people speak English?