__Caselet 3 :__In a store, there are 600 women. The store is a collection of precious stones, namely diamond, ruby, and emerald. It is found that 40% of women like diamonds, 20% of women like ruby and 10% of women like emeralds.

5% of women like
diamond and ruby. 3% of women like ruby and emerald and 4% like emerald and
diamond. 2% of women like all three stones.

Explanation :

Total number of
women = 600

Number of women who
like diamonds =

40% of total women = 40/100 x 600 = 240

40% of total women = 40/100 x 600 = 240

Number of women who
like Ruby =

20% of total women = 20/100 x 600 = 120

20% of total women = 20/100 x 600 = 120

Number of women who
like Emerald =

10% of total women = 10/100 x 600 = 60

10% of total women = 10/100 x 600 = 60

Number of women who
like diamonds & Ruby =

5% of total women = 5/100 x 600 = 30

5% of total women = 5/100 x 600 = 30

Number of women who
like diamonds &Emerald =

5% of total women = 6/100 x 600 = 24

5% of total women = 6/100 x 600 = 24

Number of women who
like Ruby& Emerald =

30% of total women = 30/100 x 600 = 18

30% of total women = 30/100 x 600 = 18

Number of women who
like diamonds, Emerald and Ruby =

2% of total women= 2/100 x 600 = 120.

2% of total women= 2/100 x 600 = 120.

Let a = diamond
only ,

b = Ruby only

c= Emerald only

d= Diamond& Ruby only

b = Ruby only

c= Emerald only

d= Diamond& Ruby only

e=Ruby &
Emerald only

f=Diamond & Emerald only

g=Diamond, Emerald and Ruby

f=Diamond & Emerald only

g=Diamond, Emerald and Ruby

Diamond => a+d+g+f = 240

Ruby
=>d+b+g+e =120

Emerald = c+f+e+g = 60

Ã° d
+ g = 30

Ã° g
+ e =18

Ã° g+
f =24

Ã° g=12

Therefore, d = 30-
12 = 18 e = 18- 12 =6

f=24-12 = 12

f=24-12 = 12

C = 60-(12+12+6)=30

b= 120 –(30+6)=84

a=240-(30+12)=198

b= 120 –(30+6)=84

a=240-(30+12)=198

__Questions with Explanations :__**Find the number of women who like both ruby and diamond.**

*1.*
a

*) 30*b) 32 c) 12 d) 6 e) 18**Answer: a**

**Explanation :**

Number of women who like both Diamond and Ruby = 30

**Find The number of women who like emerald only.**

*2.*
a)
32

*b) 30*c) 28 d) 198 e) 40**Answer: b**

**Explanation :**Number of women who like Emerald only = 30

**Find the number of women who like both diamond and emerald.**

*3.*
a) 32 b) 30

*c) 24*d) 28 e) 27**Answer: C**

**Explanation :**

Number of women who like both Diamond and Emerald = 24

**Find the number of women who like diamond only.**

*4.*
a) 60 b) 240 c) 120

*d)198*e) 84**Answer : D**

**Explanation :**

Number of women who like both only Diamond = 198

**Find the number of women who like the only ruby.**

*5.*
a) 60 b) 240 c) 120 d)
198

*e) 84*
Answer: E

Explanation :
Number of women who like only Ruby = 84

__Caselet 4.__
A colony of 5500
members, 18% of the people manage their business, and 10% of those who manage
their business are females. 65% of the total numbers of people in the colony serve
various organizations. 40% of the number of people serving various
organizations is females.

12% of the total number
of people in the colony is unemployed. 30% of the number of people in the
colon- are unemployed is females.

The remaining
people in color are children, 60% of whom are females.

*Explanation :**=*

__Number of members who manage their business__18% of total members = 18/100 x 5500 = 990

Number of females
who manage their business =

10/100 x 990 = 99

10/100 x 990 = 99

Number of males who
manage their business =

990-99 = 891

990-99 = 891

*=*

__Number of people who serve varous organizations__65% of total people = 65/100 x 5500 =3575

Number of females who
serve various organizations =

3575 x 40/100 =1430

3575 x 40/100 =1430

Number of males who
serve various organizations =

3575 – 1430 = 2145

3575 – 1430 = 2145

*=*

__Number of Unemployed people__12% of total members = 12/100 x 5500 = 660

Number of females
who are unemployed =

30% of total unemployed = 30/100 x 660 =198

30% of total unemployed = 30/100 x 660 =198

Number of males who
are unemployed = 660- 198 = 462

__Number of children :__Total members – ( People who manage their business + Serve various organization + Unemployed ) =

100% - (18% +65% +12%) = 5%

Total number of children
= 5% of total members =

5/100 x 5500 = 275

5/100 x 5500 = 275

Number of female
children = 275 x 60/100 =165

Number of male
children = 275 - 165 = 110

Total

members Male Female

members Male Female

Manage their
business 990 891 99

Serve Various
Organizations 3575 2145
1430

Unemployed 660 462 198

Children 275 110 165

__Questions and Explanation:__**The number of children (both main and females) is approximately what percent of people who manage their business (both males and females )**

*1.**a)28*b) 24 c)32 d) 21 e) 35

**Answer: A**

**Explanation:**Total number of children =275

Total number of
people who manage their business = 990

Therefore, required percentage = 275/990
x 100 =28%

**What is the difference between male and female children in the colony?**

*2.*
a) 65

*b) 55*c) 45 d) 35 e) None of these**Answer: B**

**Explanation:**Number of male children = 165

Number of female children = 110

Difference between male and female children =165–110= 55

**What is the total number of adult males in the colony (excluding the children)?**

*3.*
a) 3496 b) 3490
c)3500 d)3504

*e)3498***Answer :E**

**Explanation :**

Total number of adult males ( excluding children) =

891 + 2145 +462=3498

**What is the total number of females in the colony?**

*4.*
a)1884 b)1896 c)1888

*d) 1892*e)None**Answer : D**

**Explanation :**

Total number of females = 165 +198 +1430 +99 = 1892

**What is the respective ratio of the unemployed males to the number of males working for various organizations?**

*5.*
a) 3 :13 b) 12 : 65 c) 4:13 d) 16: 65

*e) 14:65*

**Answer :***Number of unemployed males =462*

**Explanation :**
Number of males working for
various organizations = 2145

Therefore, required
ratio = 462 : 2145 = 14 :65