Question

In a community of 175 persons, 40 reads TOI, $50$ reads the Samachar Patrika and $100$ do not read either. How many persons read both the papers?
A) $16$
B) $17$
C) $15$
D) $14$

Answer 1

In this first try to find out that the Number of people who read both the newspaper or ${\text{n(T}} \cup S{\text{)}}$ .
Hence by using the formula the people who reads both the newspaper is ${\text{n(T}} \cap S{\text{)}}$ = ${\text{n(T) + n(S)}} - {\text{n(T}} \cup {\text{S)}}$ . Number of people who read TOI $n(T)$ , Number of people who read Samachar patrika is $n(S)$

Complete step by step answer:
As in the question it is given that
Number of people who read TOI is n(T) = $40$
Number of people who read Samachar patrika is n(S) = $50$
Number of people who do not read either = $100$
Hence from the given condition Venn diagram is

Number of people who read both the newspaper ${\text{n(T}} \cup S{\text{)}}$ = Total number of people - people who don't read either
$= 175 - 100$
= $75$
Now for the people who reads both the newspaper is ${\text{n(T}} \cap S{\text{)}}$
${\text{n(T}} \cap S{\text{)}}$ = ${\text{n(T) + n(S)}} - {\text{n(T}} \cup {\text{S)}}$
${\text{n(T}} \cap S{\text{)}}$ = $40 + 50 - 75$
${\text{n(T}} \cap S{\text{)}}$ = $90 - 75$
${\text{n(T}} \cap S{\text{)}}$ = $15$

$\therefore$ There are $15$ people who read both the newspaper. Option C will be the correct answer.

Note:
In this type of question always draw the Venn diagram after that observe the question and put the values in it and proceed to the answer.
As in this question it is given as Samachar Patrika and TOI if we add one more like The Hindu newspaper then the question will become nasty and difficult to solve but it will easier if we draw a Venn diagram then it will solve easily.