Question

In a community of 250 persons ,120 read the deccan herald and 90 read the indian express and 100 do not read anything. how many persons read both deccan herald and indian express

Answer 1

60 person read both Deccan herald and Indian Express because 100 people don't read anything then 250-100=150
among 150 120 are reading deccan herlad
then 150-20=30
30 are reading Indian express then 90-30=60
so 60 person read both

Answer 2

The number of persons read both deccan herald and indian express = 60

Given :

In a community of 250 persons ,120 read the deccan herald and 90 read the indian express and 100 do not read anything

To find :

The number of persons read both deccan herald and indian express

Solution :

Step 1 of 2 :

Write down the given data

Let S = Total persons in the community

A = Persons who read the deccan herald

B = Persons who read indian express

Then, n(S) = 250 , n(A) = 120 , n(B) = 90

The number of persons who do not read anything

= n( A' ∩ B')

= 100

Step 2 of 2 :

Find number of persons read both deccan herald and indian express

n( A' ∩ B') = 100

⇒ n [( A ∪ B)'] = 100

⇒ n(S) - n( A ∪ B) = 100

⇒ 250 - n( A ∪ B) = 100

⇒ n( A ∪ B) = 250 - 100

⇒ n( A ∪ B) = 150

⇒ n(A) + n(B) - n( A ∩ B) = 150

⇒ 120 + 90 - n( A ∩ B) = 150

⇒ 210 - n( A ∩ B) = 150

⇒ n( A ∩ B) = 210 - 150

⇒ n( A ∩ B) = 60

The number of persons read both deccan herald and indian express = 60

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