Question

in a town 45% of population read magazine A, 55% read magazine B, 40% read magazine C, 30% read magazine A and B, 15% read B and C magazine. what percentage don't read any magazine?




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Answer 1

$\dag{ \underline{ \underline{ \sf{ \pmb{Question:-}}}}}$

In a town 45% of population read magazine A, 55% read magazine B, 40% read magazine C, 30% read magazine A and B, 15% read B and C magazine. What percentage don't read any magazine?

$\\ \dag{ \underline{ \underline {\sf{ \pmb{Required \: answer:-}}}}}$

$\\ \dag{ \underline{ \sf{ \pmb{Given:-}}}}$

• 45% population read magazine A
• 55% population read magazine B
• 40% population read magazine C
• 30% population read magazine A and B
• 15% population read magazine B and C

$\\ \dag{ \underline{ \sf{ \pmb{To \: find:-}}}}$

• The percentage of people who don't read any magazine.

$\\ \dag{ \underline{ \sf{ \pmb{Solution:-}}}}$

◇ Kindly see the attachment.

Here,

Number of people who read magazine A = n(A) = 45%

Number of people who read magazine B = n(B) = 55%

Number of people who read magazine C = n(C) = 40%

Now,

n(A ∩ B) = 30%

n(B ∩ C) = 15%

n(A ∩ C) = 25%

n(A ∩ B ∩ C) = 10%

Now, we know that:-

n(A U B U C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)

Substituting the values:-

= (45 + 55 + 40 - 30 - 25 - 15 + 10)%= 80%

80% population read any magazine.

Now,

The people who don't read any magazine

= U - n(A U B U C)

= (100 - 80)%

= 20%

❖Hence, 20% people don't read any magazine.

Answer 2

Answer:

20%  People don't read any magazine.

Step-by-step explanation:

n(A) = 45%; n(B) = 55%; n(C) = 40%

n(A ∩ B) = 30%; n(B ∩ C) = 15%; n(A ∩ C) = 25%

n(A ∩ B ∩ C) = 10%

n(A U B U C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)

= 45 + 55 + 40 - 30 - 25 - 15 + 10 = 80

80% population read any magazine.

Therefore,

Percentage of people who don't read magazine is (100-80)%  =  20%