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 :
1. What is the respective ratio of boys taking Painting classes to
the boys taking Singing classes?
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
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)
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
3. 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)
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%
4. What is the total number of children taking Dancing classes?
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
5. What is the number of girls taking Painting classes?
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
2. Number of Computers of Category B is approximately what per cent
of the total number of Refrigerators?
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
3. What is the average number of products in Category A together?
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
4. What is the respective ratio between the number of Televisions
of Category B and the number of Computers of Category A?
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
5. What is the difference between the number of Mobile phones of
Category B and the total number of Computers
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