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Set Theory based Questions and Solutions

Directions for Questions 1 to 4 Refer to the data below and answer the questions that follow.
In the CBSE Board Exams last year, 53% passed in Biology, 61% passed in English, 60% in Social Studies, 24% in Biology & English, 35% in English & Social Studies, 27% in Biology and Social Studies and 5% in none.
1Percentage of passes in all subjects is
A)NilC)12
B)7D)10
2If the number of students in the class is 200, how many passed in only one subject?
A)48C)46
B)more than 50D)less than 40
3If the number of students in the class is 300, what will be the % change in the number of passes in only two subjects , if the original number of students is 200?
A)more than 50%C)less than 50%
B)50.D)None of these
4What is the ratio of percentage of passes in Biology and Social Studies but not English in relation to the percentage of passes in Social Studies and English but not Biology?
A)5:7C)7:5
B)4:5D)None of these
Directions for Questions 36 and 37: Answer the questions based on the following information.
The following data was observed from a study of car complaints received from 180 respondents at Colonel Verma’s car care workshop, viz., engine problem, transmission problem or mileage problem. Of those surveyed, there was no one who faced exactly two of these problems. There were 90 respondents who faced engine problems, 120 who faced transmission problems and 150 who faced mileage problems.
5How many of them faced all the three problems?
4560
9020
6How many of them faced either transmission problems or engine problems?
3060
9040
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Directions for Questions 31 to 34: Refer to the data below and answer the questions that follow:
A newspaper agent sells The TOI, HT and IN in equal numbers to 302 persons. Seven get HT & IN, twelve get The TOI & IN, nine get The TOI & HT and three get all the three newspapers. The details are given in the Venn diagram:
31A newspaper agent sells The TOI, HT and IN in equal numbers to 302 persons. Seven get HT
A280C327
B109DNone of these
32What percent get The TOI and The HT but not The IN
Amore than 65%Cless than 60%
B@ 64%DNone of these.
33The number of persons buying The TOI and The HT only, The TOI and The IN only and The HT
and The IN only are in the ratio of
A6:4:9C6:9:4
B4:9:6DNone of these
34The difference between the number reading The HT and The IN only and HT only is
A77C78
B83DNone of these.
35A group of 78 people watch Zee TV, Star Plus or Sony. Of these, 36 watch Zee TV, 48 watch Star Plus and 32 watch Sony. If 14 people watch both Zee TV and Star Plus, 20 people watch both Star Plus and Sony, and 12 people watch both Sony and Zee TV find the ratio of the number of people who watch only Zee TV to the number of people who watch only Sony.
A9:4C3:2
B5:3D(d) 7:4

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