Question

Times, Mirror and Sun are three newspapers

(i) All readers of the Times read the Sun

(ii) Every person either reads the Sun or does not read the Mirror.

(iii) $11$ people read the Sun but do not read the Mirror

(iv) $8$ people read either the Times or the Mirror but not both.

(v) $10$ people read the Sun and either read the Mirror or do not read the Times

(vi) $14$ people either read the Sun and not the Mirror or read both the Sun and Times

(vii) $9$ people neither read the Times nor the Mirror

Number of people who read Times and Mirror both are

• A. $3$
• B. $2$
• C. $4$
• D. $5$

Answer 1

The correct option is A $3$

Time $\to T$

Mirror $\to M$

Sun $\to S$

Set $T$ is subset of set $S$

Everone either reads sun or does not read mirror for a person .

$\to$ either we reads sun as well as mirror

$\to$ or reads sun but does not reads mirror.

$\to$ or readss neither

If $M\cap T=0$

then no. of people which read $S$ $=6.5$

$x:$no.of people who read only $S$

$b:$ no. of people who read $T$ & $S$ but not $M$

$c:$ no. of people who read all three

$d:$ no. of people who read $M$ & $S$ but not $T$

$a+b=11---\left(i\right)$

$b+c=8----\left(ii\right)$

$a+c+d=10----\left(iii\right)$

$a+b+c=14---\left(iv\right)$

$\left(iv\right)$ & $\left(i\right)$

$a+b+c=a+b$

$c=14-11=3$

$c=33$

therefore,

$a=5$

$b=6$

$c=3$

$d=2$

from the

$a+x=9$

$x=9-5$

$x=9-5$

$=4$

no. of people who read only $S$ $=5$

no, of people who read $T$ & $M$ both $=3$

no. of people who read only none of them $=4$

Hence,

Option $A$ is correct answer.