**In this page set theory practice solution6 we are going to see
solution of practice questions from the worksheet set theory practice
questions2.**

**Question 6:**

**In a town 85 % of the people speak Tamil,40 % speak English and 20 %
speak Hindi. Also 32% speak English and Tamil, 13 % speak Tamil and
Hindi and 10 % speak English and Hindi, find the percentage of people
who can speak all the three languages.**

**Solution:**

**Let A,B and C are the people who speak Tamil, English and Hindi respectively.**

**Number of people who speak Tamil n (A) = 85**

**Number of people who speak English n (B) = 40**

**Number of people who speak Hindi n (C) = 20**

**Number of people who speak English and Tamil ****n (A
∩ B) = 32**

**Number of people who speak Tamil and Hindi ****n (A
∩ C) = 13**

**Number of people who speak English and Hindi ****n (B
∩ C) = 10**

**Let "x" be the number of people who speak all the three language.**

**Total number of people = **

** 100 = 40 + x + 32 – x + x +
13 – x + 10 – x – 2 + x – 3 + x **

** 100 = 40 + 32 + 13 + 10 – 2 – 3 + x **

** 100 = 95 – 5 + x**

** 100 = 90 + x **

**x = 10 % **

**(7)
An advertising agency finds that, of its 170 clients,115 use
Television,110 use Radio and 130 use Magazines. Also 85 use Television
and Magazines,75 use Television and Radio,95 use Radio and Magazines,70
use all the three. Draw Venn diagram to represent these data. Find **

**(i) how many use only Radio?**

**(ii) how many use only Television?**

**(iii) how many use Television and Magazine but not radio?**

**Solution:**

**Let A,B and C are the people who speak Television, Radio and Magazines respectively.**

**Number of people who use Television n (A) = 115**

**Number of people who ****use** Radio n (B) = 110

**Number of people who ****use** Magazine n (C) = 130

**Number of people who ****use** **Television
and Magazines**

** ****n (A
∩ C) = 85**

**Number of people who ****use** **Television and Radio**

**n (A
∩ B) = 75**

**Number of people who ****use** **Radio and Magazine**

**n (B
∩ C) = 95**

**Number of people who use all the three ****n (A ****∩ **B
∩ C) = 70

**(i) Number of people who use only Radio = 10**

**(ii) Number of people who use only Television = 25**

**(iii) Number of people who use Television and Magazine but not radio = 15**

set theory practice solution5 set theory practice solution5

**Back to worksheet****Definition****Representation of Set****Types of set****Disjoint sets****Power Set****Operations on Sets****Laws on set operations****More Laws****Venn diagrams****Set word problems****Relations and functions**

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