Question

All the people in a locality read magazines “India Today” or “The Week” or both. If \[120\]read “India Today” and \[150\] read “The Week” and \[36\] read both. Find
A) How many people are there in the locality?
B) How many people read only “India Today”?

Answer 1

Hint:
To find the number of people in the locality at first, we have to find the total number of people who read “India Today” and “The Week”. Then we will subtract the common members, that is the number of people who read both the magazines.
Again, to find the number of people who read only the magazine named “India Today” we will subtract the number by the common names.

Complete step-by-step answer:
It is given that,
The people in a certain locality read magazine named “India Today” or “The Week” or both.
Number of people who read the magazine named “India Today” is \[120\].
Number of people who read the magazine named “The Week” is \[150\].
Number of people who read both the magazines is \[36\].
We have to find out the number of people in the locality and the number of people who read only “India Today”.
To find the number of people in the locality at first, we have to find the total number of people who read “India Today” and “The Week”. Then we will subtract the common members, that is the number of people who read both the magazines.
So, the total number of people who read “India Today” and “The Week” \[120 + 150 = 270\]
Now, the number of people in the locality\[ = 270 - 36 = 234\]
Again, to find the number of people who read only the magazine named “India Today” we will subtract the number by the number of people who read both.
So, the number of people who read only the magazine named “India Today” is \[ = 120 - 36 = 84\]
Hence, we have found that
A) There are \[234\] people in the locality.
B) \[84\] People read only “India Today”.

Note:
We can solve this sum by using the Venn diagram also. For that we consider
Number of people who read the magazine named “India Today” is\[120\]. That is $n(I) = 120$
Number of people who read the magazine named “The Week” is\[150\]. That is $n(T) = 150$
Number of people who read both the magazines is\[36\]. That is $n(I \cup T) = 36$
We have to find $n(S)$where S is the number of people in the locality,
Hence$n(S) = n(I) + n(T) - n(I \cup T)$, by substituting the known values we get,
\[n(S) = 120 + 150 - 36 = 270 - 36 = 234\]
Hence the total number of peoples in the locality is\[234\].
Next to find the number of people who read only “India today” let it be $n(I')$
Where $n(I')$ is found using the following formula $n(I') = n(I) - n(I \cup T)$,
Let us substitute the known values we get $n(I') = 120 - 36 = 84$
Hence the number of people who study only “India today” is $84$.