**:**

__Caselet 1__
In a team there are
240 members (males and females). Two-thirds of them are males. Fifteen percent
of males are graduates. Remaining males are non-graduates. Three- fourths of
the females are graduates. Remaining females are non-graduates. (SBI PO 2013)

1. What is the
difference between the number of females who are non-graduates and the number
of males who are graduates?

a) 2 b)24 c)4 d)116 e) 36

2. What is the sum
of the number of females who are graduates and the number of males who are non
-graduates?

a) 184 b)96 c)156 d)84 e) 196

3. What is the ratio of the total number of males to the number of females who are
non-graduates?

a) 6:1 b)8:1 c)8:3 d)
5:2 e) 7:2

__Explanation :__
Total members (males and females)=240.

$\frac{2}{3}$ of them are males =>Males = 240 x $\frac{2}{3}$ = 160

$\frac{2}{3}$ of them are males =>Males = 240 x $\frac{2}{3}$ = 160

15% of males are
graduates =>

Male graduates= $\frac{15}{100}$ x 160 = 24

Male graduates= $\frac{15}{100}$ x 160 = 24

Male non-graduates
= 160 – 24 = 136

Number of females =
Total members – Male members = 240- 160 = 80

Three-fourth of the
females are graduates = 80 x ¾ = 60

__Questions and Answers :__
1. What is the difference between the number of females who
are non-graduates and the number of males who are graduates?

a) 2 b)24 c)4 d)116 e) 36

**Answer : C**

**Explanation :**

Number of females who are non-graduates = 80-60=20

Number of male graduates =24

Therefore, required difference = 24 -20 = 4

2. What is the sum of the number of females who are
graduates and the number of males who are non -graduates?

a) 184 b)96 c)156 d)84 e) 196

**Answer : E**

**Explanation :**

Number female graduates = 60

Number male non-graduates = 136

Required sum = 60 + 136 = 196

3. What
is the ratio of the total number of males to the number of females who are
non-graduates?

a) 6:1 b)8:1 c)8:3 d)
5:2 e) 7:2

**Answer :**

**Explanation :**Total number of males = 160

Total number of females who are non-graduates
= 20

Required ratio = 160 : 20 = 8 :1

Total number of students ( Boys + Girls ) = 400

Number of girls who speak only Hindi = 78

Number of girls who speak both the languages = 117

Therefore required ratio = 108 : 117 = 12 : 13

Number of badminton as well as Cricket players =

4 + 2 =6

Total number of children who play Badminton =

4 + 2 + 3 + 7 =16

Number of children who play Football as well as Cricket =

4 + 2 = 6

**In a school having 400 students boys and girls are in the ratio of 3:5 respectively. The students speak Hindi, English or both the languages, 12% of the boys speak only Hindi, 22% of the girls speak only English.24% of the total students speak only Hindi and the number of boys speaking both languages is 6 times the number of boys speaking only Hindi.**

__Caselet 2:__

__Explanation :__Total number of students ( Boys + Girls ) = 400

The ratio of boys to girls = 3: 5

Total students who
speak only Hindi =

24% of total students = $\frac{24}{100}$ x 400 =96

24% of total students = $\frac{24}{100}$ x 400 =96

Number of boys = 400 x $\frac{3}{8}$ = 150

Number of girls = 400 x $\frac{5}{8}$ = 250

Number of girls = 400 x $\frac{5}{8}$ = 250

Boys who speak only Hindi =>

12% of total boys = $\frac{12}{100}$ x 150 = 18

12% of total boys = $\frac{12}{100}$ x 150 = 18

Boys who speak both
English and Hindi =

6 times the number of boys speaking only Hindi =6x18=108

6 times the number of boys speaking only Hindi =6x18=108

Boys who speak only
English=150- ( 18 + 108 )

= 150 –126 = 24

= 150 –126 = 24

Girls who speak
only English =22% of total girls =

$\frac{22}{100}$ x 250 =55

$\frac{22}{100}$ x 250 =55

Girls who speak only
Hindi=

Total students who speak only Hindi - Boy who speak only Hindi =96-18=78

Total students who speak only Hindi - Boy who speak only Hindi =96-18=78

Girls who speak Hindi
and English = 250 – (78+55)=117

__Questions and Explanation:__
1.
Total how many boys speak Hindi?

a)18 b)126 c)108 d)26 e)None
of these

**Answer : a**

**Explanation :**

Number of students
who speak Hindi, then we have to take only and Hindi and (English+ Hindi)

Number of boys who speak Hindi = 18 +108 = 126

Number of boys who speak Hindi = 18 +108 = 126

2.
How many girls speak only Hindi?

a)55 b)117 c)96 d)78
e)None of these

**Answer : D**

**Explanation :**

Number of girls who speak only Hindi = 78

3.
How many total numbers of students speak English?

a)304 b)79 c)225 d)117
e)None of these

**Answer :A**

**Explanation :**Number of students who speak English = Number of students who speak only English and number of students who speak both English & Hindi

Number of students
who speak English = 24 +117 +55 +108 = 304

4.
Number of girls speaking only Hindi is what percent of the total number of
students speaking only Hindi?

a)38.2%
b)71.2% c)31.2% d)78% e)81.25%

**Answer :**

**Explanation:**Number girls speaking only Hindi = 78

Total number of students
speaking only Hindi = 78+18 = 96

Required percentage = $\frac{18}{96}$ x 100 = 18.75

5.
What is the respective ratio between the number of boys and girls speaking both
the languages?

a)23:25 b)12:25 c)12:13
d)25:13 e)None

**Answer :C**

**Explanation :**

Number of girls who speak both the languages = 117

Number of boys who speak both the languages =
108

Therefore required ratio = 108 : 117 = 12 : 13

**Caselet 3:**

Children in a class
play only one or two or all the three games Badminton, Football and Cricket. 5
children play only Cricket, 8 children play only Football and 7 children play
only Badminton. 3 children play only two games Badminton and Football, 4
children play only two games Cricket and Football and another 4 children play
only two games Badminton on and Cricket. 2 children play all the three games.

__Explanation :__
We can draw a Venn
diagram from the given information:

1. In all how many children play Football?

a) 8 b)17
c) 15 d)14 e) None of these

**Answer : b**

**Explanation :**Number of football players = 3+2+4+8 =17

2. How many children play Badminton as well
as Cricket?

a) 9 b)10
c) 4 d)6 e) None of these

**Answer : D**

**Explanation :**

Number of badminton as well as Cricket players =

4 + 2 =6

3. Total how many children are there in the
class?

a) 33 b)31 c) 36 d)35 e) None of these

**Answer : A**

**Explanation:**Total number of children in the class = 7+3+2+4+8+4+5 =33

4. In all how many children play Badminton?

a) 14 b)17 c) 12 d)13 e)
16

**Answer : E**

**Explanation :**

Total number of children who play Badminton =

4 + 2 + 3 + 7 =16

5. How many children play Football as well
as Cricket?

a) 7 b)4 c) 6 d)15 e) None of these

**Answer : C**

**Explanation:**

Number of children who play Football as well as Cricket =

4 + 2 = 6