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A newspaper agent sells the TOI, the HT and the IN in equal numbers to 302 persons. 7 persons get the HT and the IN, 12 get the TOI and the IN, 9 get the TOI and the HT and 3 get all three newspapers. Then the number of persons who get only one paper is ____

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Consider the following Venn diagram. As per the question, we need to find the sum of red areas. 

Sum of red areas= Total-Sum of blue areas-green area

Here

  • Red area=Exactly One paper
  • Blue area=Exactly Two paper
  • Green area=Exactly Three Paper

Sum of red areas = 302-(4+9+6)-3 = 302-19-3 = 302-22 = 280

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@atulcse

Here,  we have been given a Venn diagram which represents the data of the newspaper readers of three different brands...

We are asked to find the percentage of people who read TOI or HT but not NBT ...

To find that, we will first find the number of persons who read only TOI, only HT and only NBT and then reach desired result...

Formula used:

## n(A∪B∪C)

=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C)…

Complete step-by-step solution:

Given, Total number of persons who read newspaper, n(TOI∪HT∪NBT)

=302 n(HT∩NBT)

=7 ..

n(TOI∩NBT)=12 ...

n(TOI∩HT)=9 ...

n(TOI∩HT∩NBT)=3 ...

Now, using identity,

n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C)...

n(TOI∪HT∪NBT)

=n(TOI)+n(HT)+n(NBT)−n(TOI∩HT)−n(HT∩NBT)−n(TOI∩NBT)+n(TOI∩HT∩NBT) …

⇒302

=n(TOI)+n(HT)+n(NBT)−9−7−12+3 ..

Now, we are given that

n(TOI)=n(HT)=n(NBT)..

Therefore, ⇒302=3×n(TOI)−25 .…

Simplifying it, we get, ⇒n(TOI)=327/3 ...

⇒n(TOI)=109 ....

Hence, n(TOI)=n(HT)=n(NBT)=109 ...

Now, we will calculate the number of persons who read only TOI, only HT and only NBT using Venn diagram n(TOIonly) ...

=109−(6+9+3)

⇒n(TOIonly)=91 ...

Similarly, we get,n(HTonly)

=109−(6+4+3)

⇒n(HTonly)=96,

and

n(NBTonly)=109−(9+4+3)

⇒n(NBTonly)=93 …

 

 

No. of persons reading TOI or HT but not NBT is calculated as:

n(TOI or HT but not NBT)

=91+96+6

⇒n(TOI or HT but not NBT)

=193 …

Percentage of persons reading TOI or HT but not NBT

=(193/302)×100%

=63.907 …

Hence the correct , ≅64% ...

edited by

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