Question

Among $520$ members in a village, $360$ members were engaged in cattle rearing and $280$ members with poultry farming and $180$ were doing both. How many people are (i) not involved in either of the work? (ii) engaged only in poultry farming.

Answer 1

Cattle rearing, $n\left(A\right)=360$ Poultry farming, $n\left(B\right)=280$ Both, $n(A\cap B)=180$
We know, $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$
$n(A\cup B)=360+280-180$
$n(A\cup B)=360+100=460$
$\therefore$ Number of people who are engaged in the work is $460$.
(i) $\therefore$ Number of people who are not engaged in either of the work is = $520-460=60.$
$\therefore$ $60$ members of the village are not involved in either of the work.
(ii) Number of people engaged only in poultry farming $=n\left(B\right)-n(A\cap B)$
$=280-180=100$
We can represent the problem by Venn diagram.