__Caselet 5:__
In a school consisting of 2800 children, the ratio of girls to boys is 4 : 3,
respectively. All the children have taken different hobby classes viz. Singing,
Dancing, Painting, and Cooking. 20% of the boys take Painting classes.

The number of girls
taking Dancing classes is five-fourth of the number of boys taking the same.
One-fourth of the girls take Cooking classes. The total number of students
taking cooking classes is 700. Two-fifth of the boys take Singing classes, and
the remaining boys take Dancing classes.

The girls taking
Singing classes are twice the number of boys taking the same. The remaining
girls take Painting classes. (UCO
Bank PO 2009)

__Explanation :__
Total number of
children in the school = 2800

Number
of girls = 2800 x 4 /7 = 1600

Number of boys =
2800 x 3/7 = 1200

Number of boys took
Painting = 20% of total boys =

20/100 x 1200 = 240

20/100 x 1200 = 240

Total students in
cooking class = 700

Number of girls in
cooking class = ¼ of total girls =

¼ x 1600 = 400

¼ x 1600 = 400

Number boys in
cooking class = 700 – 400 = 300

Number of boys in
Singing class = 2/5 of total boys =

2/5 x 1200 =480

2/5 x 1200 =480

Number of boys in
Dancing class = 1200 – ( 240+480+300) = 180

Number of girls in
Singing class = 2 times the number of boys in Singing class

= 2 x 480 = 960

= 2 x 480 = 960

Number of girls in
Dancing classes = 5/4 of boys taking Dancing class

= 5/4 x 180 = 255

= 5/4 x 180 = 255

Number of girls
taking Painting class =

1600 – (400+960+225) = 15

1600 – (400+960+225) = 15

__Questions and Explanation :__**What is the respective ratio of boys taking Painting classes to the boys taking Singing classes?**

*1.*
a) 4:3 b)
2:1 c) 6:5 d)3:4

*e) 1:2*
Answer: E

Explanation: Number of boys taking Painting classes = 240

Number of girls taking Painting classes = 480

Therefore, required
ratio = 240 : 480 = 1 :2

**The number of girls taking Cooking classes is what percent of the total number of children in the school? (rounded off to the nearest integer)**

*2.**a) 14*b) 20 c) 6 d) 26 e) None of these

Answer: a

Explanation :
Number of girls taking Cooking classes = 400

Total number of children = 2800

Therefore, required percentage = 400/2800 x
100

= 14.28 = 14% approximately

= 14.28 = 14% approximately

**The number of boys taking Cooking classes is what percent of the total number of children in the school? (rounded off to two digits after decimal)**

*3.*
a)9.68 b)12.61

*c) 10.71*d) 8.43 e) None of these
Answer: C

Explanation :
Number of boys taking Cooking classes = 300

Total number of
children = 2800

Required percentage = 300/ 2800 x 100% = 10.71%

**What is the total number of children taking Dancing classes?**

*4.*
a) 325 b) 445
c) 390

*d) 405*e) None of these
Answer : D

Explanation :
Number of children taking dancing classes = Boys taking dancing classes + Girls
taking dancing classes = 180 + 225 =405

**What is the number of girls taking Painting classes?**

*5.*
a) 116

*b) 15*c) 125 d) 28 e) None of these
Answer: B

Explanation :
Number of girls taking Painting classes = 15

__Caselet 6:__
A company produces
four different products, viz, Mobile phones, Televisions, Refrigerators and
Computers. Each of the products has two categories viz. Category A and Category
B. The total number of all the products is 900. Twenty-five percent of the
total number of products is Computers, and one-third of the total number of
products is Televisions.

Thirty-two percent
of the total products are Refrigerators.

Fifty percent of
each of the total number of Televisions as well as the total number of
refrigerators are of Category A. Forty percent of the total number of Computers
is of Category B. One-third of the total number of Mobile phones is of Category
B.

(OBC PO 2010)

Explanation :

Total number of
products = 900.

Number of Computers
= 25% of total products =

25/100 x 900 = 225

25/100 x 900 = 225

Number of Computers
in Category B =

40% of total computers = 40/100 x 225 = 90

40% of total computers = 40/100 x 225 = 90

Number of Computers
in Category A = 225 -90 =135

Number of Televisions = 1/3 of total products =

1/3 x 900 = 300

1/3 x 900 = 300

Number of
Televisions in Category A =

50% of total Televisions = ½ x 300 =150

50% of total Televisions = ½ x 300 =150

Number of
Televisions in Category B = 300- 150 = 150

Number of Refrigerators
=

32% of total products = 32/100 x 900 =288

32% of total products = 32/100 x 900 =288

Number of Refrigerators in Category A =

50% of total refrigerators = ½ x 288 =144

50% of total refrigerators = ½ x 288 =144

Number of Refrigerators in Category B = 288- 144 =144

Number of
Televisions in Category A =

50% of total Televisions = ½ x 300 =150

50% of total Televisions = ½ x 300 =150

Number of
Televisions in Category B = 300- 150 = 150

Number of Mobile
phones = 900 – (225+300+288) =

900 – 713 = 87

900 – 713 = 87

Number of Mobile
phones in category B =

1/3 of total mobiles = 1/3 x 87 =29

1/3 of total mobiles = 1/3 x 87 =29

Number of Mobile
phones in category A = 87 -29 = 52

**Questions with Explanations :**

*1.**What is the total number of Televisions of Category A, Refrigerators of Category B and Mobile phones of Category B together?*

*a) 225 b)323 c) 325 d)223 e) None of these*

Answer
: B

Explanation
:

Number of Televisions of Category A = 150

Refrigerators
of Category B = 144

Mobile
phones of Category B =29

Required Value = 150+ 144 + 29 = 323

**Number of Computers of Category B is approximately what per cent of the total number of Refrigerators?**

*2.*
a) 29

*b) 31*c) 37 d) 43 e) 47
Answer
: B

Explanation
: Number of Computers of category B = 90

Total
number of Refrigerators = 288

Required percentage = 90/288 x 100 % =
31.25% = 31% approximately

**What is the average number of products in Category A together?**

*3.*
a)110.25
b)115.5

*c)121.75*d)102 e)106
Answer : C

Explanation :

Total number of products of Category A together = 58+ 135+144+150=487

Total number of products of Category A together = 58+ 135+144+150=487

The average number of products of Category A
together = 487/4 = 121.75

**What is the respective ratio between the number of Televisions of Category B and the number of Computers of Category A?**

*4.*
a)3:5 b)5:3

*c)10:9*d)5:6 e)None of the above
Answer: C

Explanation: Number
of Televisions of Category B =150

Number of Computers
of Category A =135

The respective ratio between the number of
Televisions of Category B and the number of Computers of Category AS = 150: 135
= 10:9

**What is the difference between the number of Mobile phones of Category B and the total number of Computers**

*5.*
a) 146 b) 176 c) 167 d)
156

*e)196*
Answer: E

Explanation: Number of Computers (Both Category A and Category B) =
225

Number of Mobile phones of
Category B = 29

Difference
between the total number of Computers and number of Mobile phones of Category B
= 225 – 29 = 196