# In a town of 10000 families, it was found that 40% families buy product A, 20% buy product B

#### DAVV MBA PYQ

In a town of 10000 families, it was found that 40% families buy product A, 20% buy product B and 10% buy product C, 5% buy product A and product B, 3% buy product B and product C and 4% buy product A and product C. If 2% families buy product A, B, C all. Then find the number of the families buy product A only.
Solution:
Formula:
n(A U B U C) = n(A)+n(B)+n(C)-n(A ∩ B)-n(A ∩ C)-n(B ∩ C)+n(A ∩ B ∩ C)
Given,
n(A U B U C) = 10000
n(A) = 4000
n(B) = 2000
n(C) = 1000
n(A ∩ B ∩ C) = 200
n(A ∩ B) = 500
n(A ∩ C) = 400
n(B ∩ C) = 300
Number of the families buy product A only ?
From the Venn diagram,
Number of the families by product A only = 3300.

#### 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.
Q2. In a survey of 500 T.V. viewers, 285 watched KBC, 195 watch cricket, 115 watch hockey, 45 watch KBC and hockey, 70 watch KBC and cricket, 50 watch cricket and hockey, 50 do not watch any of three games. How many watch all 3 and how many watch exactly one of three ?