# In a city there are 100000 people, 64% of them speak Greek, 55% people speak Latin, 43% p

#### DAVV MBA PYQ

In a city there are 100000 people, 64% of them speak Greek, 55% people speak Latin, 43% people speak French, 21% people speak both Greek and Latin, 31% people speak both Greek and French, and 41% people speak both Latin and French. Determine the number of people speak all the three languages.
Solution:
G for Greek
L for Latin
F for French
Formula:
n(G U L U F) = n(G)+n(L)+n(F)-n(G ∩ L)-n(G ∩ F)-n(L ∩ F)+n(G ∩ L ∩ F)
Given,
n(G U L U F) = 100000
n(G) = 64% = 64000
n(L) = 55% = 55000
n(F) = 43% = 43000
n(G ∩ L ∩ F) = ?
n(G ∩ L) = 21% = 21000
n(G ∩ F) = 31% = 31000
n(L ∩ F) = 41% = 41000
n(G U L U F) = n(G)+n(L)+n(F)-n(G ∩ L)-n(G ∩ F)-n(L ∩ F)+n(G ∩ L ∩ F)
100000 = 64000+55000+43000-21000-31000-41000+n(G ∩ L ∩ F)
n(G ∩ L ∩ F) = 31000
Number of people speak all the three languages = 31000.

#### Practice questions (DAVV MBA PYQs):

Q1. In a city there are 100000 people, 64% of them speak Greek, 55% people speak Latin, 43% people speak French, 21% people speak both Greek and Latin, 31% people speak both Greek and French, and 41% people speak both Latin and French. Determine the number of people speak all the three languages.