You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Venn Diagram

There was a s...

Question

There was a survey in a city about number of people reading newspaper A, B and C. There are 42% of people read newspaper A; 51% of people read newspaper B and 68% of people read paper C. 30% of people read both newspaper A and B. 28% reads B and C and 36% read C and A. 8% do not read any newspaper. Find the percentage of people who read all the three newspapers.

__

Open in App

Solution

Given survey data

n(A) = percentage of people read newspaper A = 42%

n(B) = percentage of people read newspaper B = 51%

n(C) = percentage of people read newspaper C = 68%

n(A∩B) = percentage of people read newspaper A and B = 30%

n(B∩C) = percentage of people read newspaper B and C = 28%

n(C∩A) = percentage of people read newspaper C and A = 36%

since, its given 8% people do not read any newspaper

percentage of people read newspaper = Total people - people don't read newspaper

n(AUBUC) = 100% - 8% = 92%

we know,

n(AUBUC) = ∑ n(A) - ∑ n(A∩B) + n(A∩B∩C)

92 = 42 + 51 + 68 - 30 - 28 - 36 + n(A∩B∩C)

92 = 161 - 94 + n(A∩B∩C)

92 = 67 + n(A∩B∩C)

n(A∩B∩C) = 92 - 67 = 25%

Percentage of people who read all the three newspapers = 25%

Suggest Corrections

Similar questions

There was a survey in a city about number of people reading newspaper A, B and C. There are 42% of people read newspaper A; 51% of people read newspaper B and 68% of people read paper C. 30% of people read both newspaper A and B. 28% reads B and C and 36% read C and A. 8% do not read any newspaper. Find the percentage of people who read all the three newspapers.

Q. In a city, three daily newspapers

A, B, C

are published.

42

% of the people in that city read

A

51

% read

B

and

68

% read

C

30

% read

A

and

B

;

28

% read

B

and

C

;

36

% read

A

and

C

;

8

% do not read any of the three newspapers. The percentage of persons who read all the three papers is

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I and 3 read all three newspapers, find

(i) the number of people who read atleast one of the newspapers.

(ii) the numbers of people who read exactly one newspaper.

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I,11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find:

(i) the number of people who read at least one of the newspapers.

(ii) the number of people who read exactly one newspaper.

In the city,50% people read newspaper A,45% read newspaper B, and 25% read neither A nor B. What percentage of people read both the newspaper A as well as B

Join BYJU'S Learning Program