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Caselet 5:   In a school consisting of 2800 children, the ratio of girls to boys is 4 : 3, respectively. All the children have taken dif...

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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
Total students in cooking class = 700
Number of girls in cooking class = ¼ of total girls = 
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
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
Number of girls in Dancing classes = 5/4 of boys taking Dancing class 
= 5/4 x 180 = 255
Number of girls taking Painting class = 
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

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
Number of Computers in Category B = 
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
Number of Televisions in Category A = 
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
Number of Refrigerators in Category A = 
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
Number of Televisions in Category B = 300- 150 = 150

Number of Mobile phones = 900 – (225+300+288) = 
900 – 713 = 87
Number of Mobile phones in category B =
 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
     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