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Caselet 9:  In a school 800 students have visited five different cities viz. Delhi, Ajmer. Varanasi, Mumbai, and Jodhpur. Fifty-four per...

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Caselet 9: 
In a school 800 students have visited five different cities viz. Delhi, Ajmer. Varanasi, Mumbai, and Jodhpur. Fifty-four percent of the total students are boys. One-fourth of the total number of girls visited Mumbai. Twenty-five percent of the total number of girls visited Delhi. Number of girls who visited Jodhpur is half the number of girls who visited Delhi.
Five-sixth of the remaining girls visited Ajmer. Total number of students who visited Mumbai is 192. One-fourth of the total number of boys visited Varanasi. 101 boys have visited Ajmer. Two-third of the remaining number of boys has visited Delhi.

Data Interpretation and Analysis

Total number of students = 800
Total number of boys = 54% of total students = 54/100 x 800 = 432
Total number of girls =800 – 432 = 368
Girls
Girls who visited Mumbai =1/4 of total girls = ¼ x 368 =92
Total number of girls who visited Delhi = 25% of total girls = 25/100 x 368 =92
Number of girls who visited Jodhpur= ½ of total number of girls who visited Delhi
= ½ x 96 =46
Remaining girls = 368- (92+92+48)=368-230=138
Total number of girls who visited Ajmer = 5/6 of remaining girls = 138 x 5/6 =115
Total number of students who visited Varanasi = 368 - (230+115) =368 – 345 =23

Boys
Total number of boys = 54% of total students = 54/100 x 800 = 432
Total number of students who visited Mumbai = 192
Boys who visited Mumbai = 192- 92 = 100

Total number of boys visited Varanasi = ¼ of total boys = ¼ x 432 = 108
Total number of boys who visited Ajmer =101
Remaining Boys = 432 –(100+101+108) = 432 – 309 =123
Total number of boys who visited Delhi = 2/3 of remaining boys =2/3 x 123 = 82
Total number of boys who visited Jodhpur = 432 – (309+82)=41

Questions and Answers on give Caselets in Data Interpretation:

1.    What is the respective ratio between the number of girls who visited Delhi and number of boys who visited Mumbai?
a) 23 : 24 b) 23 :50   c) 23 : 25 d) 50 : 23 e) None
Answer: C
Explanation : Number of girls who visited Delhi=92
Number of boys who visited Mumbai= 100
   Therefore, required ratio = 92 :100  = 23 :25

2.    What is the average number of boys who visited Delhi, Varanasi, and Jodhpur together?
a) 82       b) 77       c) 86           d) 76   e) None of these
Answer: b
Explanation: Number of boys who visited Delhi= 82
Number of boys who visited Varanasi = 108
Number of boys who visited Jodhpur = 41
   Average number of boys who visited Delhi, Varanasi and Jodhpur = (82+108+41)/3 =231/3 =77

3.    What is two-third of the total number of girls who visited Jodhpur and Varanasi together
a) 46       b) 48           c) 54    d) 58     e) None
Answer: A
Explanation: Total number of girls who visited Jodhpur=46
Total number of girls who visited Varanasi = 23
 2/3rd of the total number of girls who visited Jodhpur and Varanasi = 2/3 (46+23)=2/3 x 69 =46

4.    Total number of students visited Jodhpur is approximately what percent of the number of girls who visited Ajmer?
a) 90       b) 81   c) 66   d) 70       e)76
Answer: E
Explanation: Number of students who visited Jodhpur = (46+41)=87
  Number of girls who visited Ajmer = 115
     Required percentage = 87/115 x 100% = 75.65% = 76% approximately

5.    What is the total number of students who visited Varanasi?
a) 121      b) 143 c) 111 d) 153     e)131
Answer: E
Explanation :
          Number of boys who visited Varanasi = 108
Number of girls who visited Varanasi=23
     Total number of students who visited Varanasi = 108 + 23 =131


Case let 10:
In a school, 1200 students have visited five different cities viz. Delhi, Kolkata, Varanasi, Mumbai, and Jodhpur.
Forty-five percent of the total students are boys. Thirty percent of the total girls visited Mumbai. Two-fifth of the total girls visited Delhi. The number of girls who visited Jodhpur is half of the girls visited Delhi.
Two third of the remaining girls visited Kolkata. Total number of students who visited Mumbai is 300. Twenty percent of the total boys visited Delhi. Forty percent of the total boys visited Jodhpur. An equal number of boys visited Kolkata and Varanasi.
(BOB PO 2010)
Data Analysis and Interpretation:
  Total number of students = 1200
Girls
Total number of girls =(100% -45%) =55% of total students = 55/100 x 1200 =660
Number of girls who visited Mumbai  = 30% of total girls = 30/100 x 660 =198
Number of girls who visited Delhi= 2/5th of total girls = 2/5 x 660 = 264
Number of girls who visited Jodhpur= ½ of the number of girls who visited Delhi = 264/2 =132
Girls who visited Kolkata = 2/3rd of remaining girls = 2/3 x (660 – (198+264+132))
                                                = 2/3 x 66 =44
Number of girls who Varanasi =660-(198+264+132+44)=22
Boys :
Total number of boys = 45% of total students = 5/100 x 1200 =544
Number of boys who visited Delhi = 20% of total students = 20/100 x 540 =108
Boys who visited Jodhpur = 40% of total boys = 40/100 x 540 = 216
Boys who visited Mumbai = Total students who visited Mumbai – Girls who visited Mumbai
                                                =300-198 = 102
Remaining boys = 540 – (108+216+102) = 540-426 = 114
Equal number of boys visited Varanasi and Kolkata
Number of boys who visited Kolkata = 114/2 = 57
Total number of boys who visited Varanasi = 114/2 = 57

Questions and Explanations for the above case let in data interpretation questions:

1.    What is the total number of girls who visited Delhi, Mumbai and Varanasi together?
a)464       b)484  c)536  d)556  e)None of these
Answer: B
Explanation: Number of girls who visited Mumbai =198
Number of girls who visited  Delhi= 264
Number of girls who visited Varanasi = 22
     Required total number of girls = 198 +264+22 = 484

2.    Total number of students who visited Jodhpur is approximately what percent of the number of girls who visited Delhi?
a)111       b)91          c)132     d)32    e)72
Answer: C
Explanation: Total number of students who visited Jodhpur ( Both boys and girls )
                    = 216 +132 = 348
Total number of girls who visited Delhi = 264
      Therefore, required percentage = 348/246 x 100% = 131.81 = 132% approximately

3.    What is the average number of boys who visited Kolkata, Varanasi and Jodhpur together?
a)110       b)122  c)101  d)104  e)None of these
Answer: A
Explanation: Number of boys who visited Kolkata=57
Number of boys who visited Varanasi = 57
Number of boys who visited Jodhpur = 216
The average number of boys who visited Kolkata, Varanasi, and Jodhpur together = (57+57+216)/3 = 110

4.    What is the total number of students who visited Varanasi?
a)78        b)69    c)102  d)103  e)79
Answer: E
Explanation: Number of boys who visited Varanasi = 57
Number of girls who visited  Varanasi = 22
    Total number of students who visited Varanasi = 57 + 22 =79

5.    What is the respective ratio between the number of girls who visited Kolkata and the number of boys who visited Mumbai?
a)22:51    b)23:51            c)21:55    d)51:22 d)None
Answer: A
Explanation: 
Number of girls who visited Kolkata = 44
Number of boys who visited Mumbai = 102

    Required ratio = 44 : 102 = 22:51