Question:
A town has total population $25000$, out of which $13000$ read ??he Hindustan Times and $10500$ read ??he Indian Express?
A town has total population $25000$, out of which $13000$ read ??he Hindustan Times and $10500$ read ??he Indian Express?
Updated On: Jul 6, 2022
- $10\%$
- $16\%$
- $27\%$
- $30\%$
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The Correct Option is B
Solution and Explanation
Let $X$, $A$ and $B$ be the sets of all persons, persons reading ??he Hindustan Times?
$\therefore n(X) = 25000$, $n(A) = 13000$, $n(B) = 10500$,
$n(A \cap B) = 2500$
We have, $n(A \cup B) = n(A) + n(B) - n(A \cap B)$
$= 13000 + 10500 - 2500 = 21000$
$\therefore$ Number of persons not reading any newspaper
$= n(X) - n(A \cup B) = 25000 - 21000 = 4000$
Required percentage $= \frac{4000}{25000} \times 100 = 16\%$
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Concepts Used:
Sets
Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.
Example of set: Set of vowels A={a,e,i,o,u}
Representation of Sets
There are three basic notation or representation of sets are as follows:
Statement Form: The statement representation describes a statement to show what are the elements of a set.
- For example, Set A is the list of the first five odd numbers.
Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.
- For example represent the set of vowels in roster form.
A={a,e,i,o,u}
Set Builder Form:
- The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
- The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
- For example, A = { k | k is an even number, k ≤ 20}. The statement says, all the elements of set A are even numbers that are less than or equal to 20.
- Sometimes a ":" is used in the place of the "|".