A survey was conducted among 100 students in a class who read detective novels written by Conan Doyle or Agatha Christie or both. Due to some recording error in the computer most of the figures were missing. The following table shows the remaining data. Doyle Christie Both Total Male Female 40 Total 70 100 Further, it is known that (1) 37% of the students read both Doyle and Christie. (2) The ratio of males to females is 1 : 1. (3) 50% of the females read books of both the authors. 9. How many males read books by both the authors? (1) 10 (2) 12 (3) 37 (4) 45 10. How many students read books by only Christie? (1) 70 (2) 10 (3) 33 (4) 23 11. How many females read books by only Doyle? (1) 25 (2) 40 (3) 35 (4) 15 12. How many students do not read books by both the authors? (1) 12 (2) 27 (3) 37 (4) 63
Answers
Given : A survey was conducted among 100 students in a class who read detective novels written by Conan Doyle or Agatha Christie or both.
Due to some recording error in the computer most of the figures were missing.
it is known that
(1) 37% of the students read both Doyle and Christie.
(2) The ratio of males to females is 1 : 1.
(3) 50% of the females read books of both the authors.
To Find : Complete Table
How many males read books by both the authors
(1) 10 (2) 12 (3) 37 (4) 45
How many students read books by only Christie
(1) 70 (2) 10 (3) 33 (4) 23
How many females read books by only Doyle
(1) 25 (2) 40 (3) 35 (4) 15 12.
How many students do not read books by both the authors
(1) 12 (2) 27 (3) 37 (4) 63
Solution:
Doyle Christie Both Total
Male
Female 40
Total 70 100
37% of the students read both Doyle and Christie.
=> BOTH total = 37
Doyale total + Christie total - Both total = Total
=> Doyale total + 70 - 37 = 100
=> Doyale total = 67
Doyale female = 40
=> Doyale male = 67 - 40 = 27
The ratio of males to females is 1 : 1. =>
Males Total = 50 , Females Total = 50
50% of the females read books of both the authors
=> 25 females read books of both the authors
BOTH total = 37
=> Both Male = 37 - 25 = 12
Doyale Male + Christie Male - Both Male = Total Male
=> 27 + Christie Male - 12 = 50
=> Christie Male = 35
Doyale Female + Christie Female - Both Female = Total Female
=> 40 + Christie Female - 25 = 50
=> Christie Male = 35
Complete table is as Below:
Doyle Christie Both Total
Male 27 35 12 50
Female 40 35 25 50
Total 67 70 37 100
12 males read books by both the authors
70 - 37 = 33 students read books by only Christie
40-25 = 15 females read books by only Doyle
100-37 = 63 students do not read books by both the authors
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